I search for dictionary of Georgian with lexical stress, but i can't find online of offline. Perhaps Georgian have any explicit rules for lexical stress which i don't know?
Aronson (1990) gives the following rules for stress-assignment in Georgian:
less than 4 syllables in word -> stress on 1st OR antepenultimate syllable
5 or more syllables in word -> stress on 1st AND antepenultimate syllables
Robins & Waterson (1952) give an alternative, less compact (but perhaps more readable) set of rules:
2 syllables -> stress on 1st syllable
3 syllables -> stress on 1st OR 2nd syllable
4 syllables -> stress on 2nd OR on 1st & 3rd syllables
5 syllables -> 1st & 3rd OR 2nd & 4th syllables
6+ syllables -> 1st & antepenultimate syllables
Not being overly familiar with Georgian, i can't speak to the accuracy of each, but i suspect the more recent 1990 reference is the one to go with. So, by way of an answer to your question: Georgian stress-assignment is partially rule governed. Applying the rules helps, but since at least one of the rules is disjunctive, stress assignment must be partially lexicalised.