Definition and Greek equivalent
The word translated as "Lily" is šûšan. It is the origin of the English name "Susan".
In the 1950s-1980s, many insisted a white lily was meant by šûšan - for this view, see Mordechai Cogan's commentary on 1 Kings4. However more recent scholarship tends to favor the hypothesis that this is a loanword. Here is one of the best experts at ANE iconography, Othmar Keel, in the Continental Commentary1:
The Hebrew word שֹׁושׁנה or שֹׁושׁן is borrowed from Egypt, where it
clearly means the water lily or lotus. Nevertheless, most translators
have preferred simply “lily,” arguing that Israel had no water lilies.
But they are wrong; even today one can find there the white water lily
(Nymphaea alba L.), common also in Europe, and the sweet-smelling
African blue water lily (Nymphaea caerulea Savigny). When Sharon was
full of marshes, there would have been more water lilies than today.
But there is an even better argument for translating שֹׁושׁנה as
“water lily” or “lotus.” The OT reports that the brim of the molten
sea took the shape of the שֹׁושׁן (1 Kgs 7:26*). Vessels in the form
of lotus blossoms (like the chalice in fig. 31) are known both in
Egypt and in Israel but there are none in the form of lilies. One also
reads of capitals in שֹׁושׁן form (1 Kgs 7:19*, 22*). All kinds of
lotus capitals have been found (fig. 32), but no lily capitals. At
least some scholars who equate שֹׁושׁנה with the lily admit that in
these technical expressions relating to construction שֹׁושׁנה means
lotus, but not, they say, in the Song. They follow the translators of
the Hebrew Bible into Greek, who rendered שֹׁושׁנה with κρίνον (lily).
But the latter were merely conforming the OT to the Greek world, as
Herodotus, the first famous Greek tourist in Egypt, had already done
(ca. 450 B.C.): “When the river is in flood and overflows the plains,
many lilies, which the Egyptians call lotus, grow in the water.”[Herodotus 2.92; tr. A. D. Godley, Herodotus, vol. 1, rev. ed., LCL (Cambridge, Mass.: Harvard Univ. Press, 1926, 1966) 377.]
The Theological Dictionary of the Old Testament takes a middle ground2, accepting that šûšan is a loanword from Egyptian ššn/šwšn which means lotus flower, but arguing that in Hebrew, it can refer to either a rose, or lily, or any flower with a bell shaped blossom, and sometimes to all flowers. In Syriac šawšantāʾ means only "lily", and in Arabic sausan refers to iris.
As in the New Testament, reference is made to "the lily[κρίνον] of the field", and as there is no other known word that specifically means "lily" in Biblical Hebrew, I will accept the TDOT definition going forward and assume that this is the flower that was meant in the gospels as well. E.g. that κρίνον has Hebrew equivalents שׁוּשַׁן,פֶּ֫רַח and חֲבַצֶּ֫לֶת. This is the standard view of analytical lexicons2
Fun Fact: where many older bibles translate "the rose [חֲבַצֶּ֫לֶת] of Sharon", most modern lexicons gloss this as crocus or asphodel. If really a rose was meant, the word would most likely be šûšan. But getting plants and animals right is often difficult for translators of ancient texts, and scholars continue to debate this.
Symbolic Meaning
In Egypt, the lotus was the primary symbol of regeneration and this meaning was also carried over to Palestine5:
In the first millennium B.C. the lotus was one of the favorite symbols
in the region stretching from Egypt to Syria. On small objects of
Egyptian and Phoenician art, like ivory carvings, metal work (fig.
33), scarabs, and other seal amulets (fig. 34), one finds the sun-god
as a child sitting in a lotus blossom. In Egyptian mythology the lotus
represents the transition from the dark primeval waters to the ordered
world. It is a primary symbol of the Egyptian idea of regeneration. At
every opportunity, Egyptian gods and human beings—living and
dead-smell lotus flowers in order to capture their regenerative
powers, to become as young and fresh as the sun-god at dawn. People in
Palestine/Israel were also familiar with this custom, as shown, for
example, by scarabs (figs. 35–36), ivories (cf. fig. 64), and wall
paintings (fig. 37). In Egypt the head of a person who had died was
portrayed in a lotus flower so that the person might go forth from it
like the morning sun, new and rejuvenated (fig. 38). Even now, the
water lily, opening out of the water in all its radiance, serves to
symbolize the freshness provided by soaps, bath accessories, and
cosmetics of all kinds. When a woman in an ancient Egyptian love song
calls her beloved “my lotus,”[Cairo Love Songs, group A, no. 20C; tr. Fox, 32.] or when the woman here calls herself a
lotus flower, it means they are able and willing to bestow renewed
power—“Love’s sweet breath—a new-born life.”
As a result, the sexual references in the Song of Solomon involving lilies can be interpreted as references to fertility and thus the bringing forth of new life.
But more interesting is the comparison of the Lily to the (female beloved) - that is, God's people, who are then also assumed to be imbued with new life - born again.
Hosea 14:5 (LEB)
I will be like the dew to Israel;
he will blossom like the lily plant,
and he will strike his roots like the trees of Lebanon.
The explicit association to the beloved as a lily can also be seen in Song of Solomon:
[Bride] I am the rose of Sharon,
And the lily of the valleys.
[Groom] As the lily among thorns,
So is my love [beloved] among the daughters.
- Song of Solomon 2:1–2 (KJV 1900)
The bride is among thorns (that can choke the beloved). The thorns are analogous to the other daughters, the ones that aren't chosen by the groom and are not given new life - thus to the world out of which the bride is chosen.
Moreover the groom dwells among the lilies [Song 2.16, 6.2] and he gathers the lilies to himself [Song 6.2], so God can be found dwelling among those who have the new life, which is why the temple was decorated with lilies.
In the Parable of the Sower, the "thorns" are identified as the cares of the world [Luke 8.14]. These choke the new life. This can be seen in the story of Mary and Martha:
Luke 10:38–42 (LEB)
38 Now as they traveled along, he entered into a certain village. And
a certain woman ⌊named⌋ Martha welcomed him. 39 And ⌊she had⌋ a sister
named Mary, who also sat at the feet of Jesus and was listening to
his teaching. 40 But Martha was distracted with much preparation, so
she approached and said, “Lord, is it not a concern to you that my
sister has left me alone to make preparations? Then tell her that she
should help me!” 41 But the Lord answered and* said to her, “Martha,
Martha, you are anxious and troubled about many things! 42 But few
things are necessary, or only one thing, for Mary has chosen the
better part, which will not be taken away from her.”
Mary was like the lily, at rest with her beloved, neither toiling nor spinning [Luke 12.27], whereas Martha was running around, seeing only the cares of the world and not resting with Christ. But God only dwells among those who have new life because the new life is God dwelling in them, and the indwelling occurs for those who do not toil or spin. For them, he renews and becomes their strength, which is why the pillars of the temple whose names were related to God's support and strength were adorned with lilies.
Referenced Figures
The images and text of descriptions below are from Keel's commentary:
- Figure 31: Egyptian Chalice in the form of a Lotus blossom, circa 1500 BC.

- Figure 32: Two capitals in the form of lotus blossoms (left, from the mortuary structure of Ptahshepses in Abusir, between 2500 and 2350 B.C.; right, from the palace of Apries in Memphis, between 590 and 570 B.C.)

- Figure 33: The young sun-god, with the sun disk overhead, sits on the opened primeval lotus, the symbol of the powers that can overcome death and chaos. (He is meant to be within the flower.) The finger in his mouth and the side curl shows him to be a child; the scepter in his right hand show him to be the ruler. He is flanked by two protecting asps. (Bracelet of a son of Pharaoh Sheshonk I, mentioned in 1 Kgs, 14:25; ca. 930 B.C.)

- Figure 34: The young sun-god, seated on the lotus, is also portrayed on a seal that, according to the inscription on the opposite side (not pictured), belonged to a man with the typical Judean name “Asyo, son of Yokim.” ‘asyo means “Yahweh made”; yoqim, “Yahweh let arise” (eighth/seventh century B.C.)

Figure 35: While walking, a man smells a large lotus blossom; its aroma is life renewing (cf. fig. 150). (Scarab from Beth-shan; ca. 1400 B.C.)

Figure 36: A seated man smells a very large lotus blossom. (Scarab from Beth-shemesh; between 1000 and 800 B.C.)

- Figure 37: A man on a throne smells a lotus blossom. (Wall painting from Kuntillet ‘Ajrud; ca. 800 B.C.)

- Figure 38:The head of Tutankhamen emerges from a lotus flower. The head of the dead person was portrayed in the primeval lotus so that, in analogy to the sun (figs. 33 and 34), he might break forth from it filled with renewed vitality. (Wood sculpture overlaid with plaster and painted; tomb of Tutankhamen, ca. 1325 B.C.) This same motif occurs frequently in the death papyri.

- Figure 64:Fig. 64. A Canaanite king, returned from a victory, seated on his cherub throne. The princess (cf. figs. 39 and 40) offers him a lotus blossom and a towel. The musician at the right plays the lyre, while, at the left, two servants draw wine from a large mixing vessel. (Ivory engraving from Megiddo; ca. 1300 B.C.) the actualization of a happy situation and 2:17 expresses the wish to experience this happiness again and again (the move from indicative to imperative implies a connection). In content, the “grazing” of 2:16 and the gazelle comparison of 2:17d unite the two parts. Verse 17c–f occurs again in 8:14, although with a significant variation (“make haste,” i.e., flee, instead of “turn,” i.e., return). The connections in 8:14 are too opaque to be of any help in a decision here.

Othmar Keel, A Continental Commentary: The Song of Songs (Minneapolis, MN: Fortress Press, 1994), 78.
H. Schmoldt, “שׁוּשַׁן,” ed. G. Johannes Botterweck, Helmer Ringgren, and Heinz-Josef Fabry, trans. Douglas W. Stott, Theological Dictionary of the Old Testament (Grand Rapids, MI; Cambridge, U.K.: William B. Eerdmans Publishing Company, 2004), 553.
The Lexham Analytical Lexicon to the Greek New Testament (Logos Bible Software, 2011).
Mordechai Cogan, I Kings: A New Translation with Introduction and Commentary, vol. 10, Anchor Yale Bible (New Haven; London: Yale University Press, 2008), 263.
Keel, p.80.