The Medieval manuscripts of Sirach contain an unusual feature.
An example elsewhere in Sirach
For example, Cairo manuscript B XII recto contains the text of Sirach 42.16:
(Scan from Cambridge University, via bensira.org.)
שמש ֯ זורחת על כל נגלתה [[ ]] וכבוד ייי על כל מעשיו׃
The rad[ia]ting sun is reveal[ed] over everything [[ ]] and the glory of yyy over all his works.
The Dead Sea Scroll manuscript Masada V, about a thousand years older, reads:
(Composite of scans from bensira.org and deadseascrolls.org.il.)
שמש זהרת על כל נגלת [[ ]] [כ]בוד אדני מלא מעשיו
The sun, shining over all, reveals itself [[ ]] the glory of the Lord fills his creation.
These each corresponding to the LXX:
ἥλιος φωτίζων κατὰ πᾶν ἐπέβλεψεν καὶ τῆς δόξης κυρίου πλῆρες τὸ ἔργον αὐτοῦ
The shining sun looked down upon everything, and its work is full of the glory of the Lord.
This would suggest that the Hebrew vorlage of Sirach originally mentioned Yahweh (יהוה), but the Tetragrammaton was replaced in one manuscript tradition with 'Lord' (אדני in Masada V, κυρίου in the LXX), but in another manuscript tradition with an obvious, ineffable euphemism (ייי).
Bearing on Sirach 51.10
As Susan pointed out in her comment, this triple-Yod appears in Sirach 51.10 of B XX verso of the Cairo manuscript:
And I raised up an acclamation, 'O yyy, you are my father [[ ]] for you are my mighty salvation!
Do not forsake me in the day of distress [[ ]] in the day of disaster and desolation.'
B XX verso is in good condition (unlike the two examples provided above), so we have no reason to suspect the translation provided is in error. This means the text of Sirach 51.10 contains a variant between the Cairo manuscript and the LXX.
In either text, a speaker is addressing yyy/the Lord, in prayer. This first 'lord' must God. Hence, the 'father of my lord' in the LXX is also referring to God.
The second 'lord' in the LXX may then be a reference to a royal figure. This would be a similar case to Psalm 110.1, which in Hebrew reads 'Yahweh said to my lord', while the LXX has 'The Lord said to my lord'.