Although I doubt the difference is there in the original language, it seems to me the translators are correct to give the two references different articles - at least in the ESV, all the references in Genesis and Revelation are translated with the definite article, including the very first:
9And out of the ground the LORD God made to spring up every tree that is pleasant to the sight and good for food. The tree of life was in the midst of the garden, and the tree of the knowledge of good and evil. Genesis 2:9 ESV
Just as there is a difference between "a god" and "The God", "The Tree of Life" is the ultimate form of "a tree of life" - so they are similar in nature and effect, but one is the ultimate expression and the other is a subordinate concept - the degree of subordination must be inferred from the context. In the case of Proverbs 11:30, the exegetical question is whether "the righteous/wise" save lives just in the literal sense, or whether the concept of 'eternal life' (which is a quality of life, not just a duration) is entangled and to what degree.
I would lean towards the literal sense because of the genre of Proverbs - that seems to be the sense in chapter 3 ('She' refers to 'wisdom' in the verse 18):
18She is a tree of life to those who lay hold of her;
those who hold her fast are called blessed. ESV
21My son, do not lose sight of these—
keep sound wisdom and discretion,
22and they will be life for your soul
and adornment for your neck.
23 Then you will walk on your way securely,
and your foot will not stumble.
24 If you lie down, you will not be afraid;
when you lie down, your sleep will be sweet.
25 Do not be afraid of sudden terror
or of the ruin of the wicked, when it comes,
26for the LORD will be your confidence
and will keep your foot from being caught. ESV