Be aware that the following is only an educated guess.
Even ignoring the unconventional stress, lebendig is a peculiar word. It is the only German word formed this way¹, i.e., by appending ig to the present participle. Usually such adjectives are formed by appending an adjective ending to the basic stem (here, leb), as for example in lebhaft, wendig, möglich.
Relatedly, there are only few adjectives that²:
- have three syllables;
- end on a standard stem such as ig or lich;
- have no sort of morpheme boundary between the first two syllables, such as in ge-bräuch-lich or in-halt-lich;
- are not reduced in spoken language, such as hügelig → hüglig.
Many of those are based on loanwards, which are exempt from the stress rules anyway and are at times also stressed on the second syllable, e.g., persönlich. Moreover, only very few such words have a similar vowel sequence as lebendig, namely ehelich, elterlich, flehentlich, leserlich, schwesterlich and wesentlich, all of which are not unique in their formation. Finally, there are only three other such words ending on ig, namely heimelig, morastig, minütig (the latter two are based on loanwords and stressed on the second syllable). So, the vast majority of three-syllable adjectives is stressed on the second syllable.
Due to this lack of parallels, speakers could have started ignoring the origin of the word and stressing it in analogy to the many three-syllable adjectives starting with a prefix such as behändig, gebrechlich or verlässlich. This may be helped by the word starting with the typical prefix vowel e.
¹ All other German words ending with endig are derived from wendig and not from a present participle of a verb. Perhaps wissentlich has a comparable origin.
² Taking all three-syllable words from a dictionary ending on lich or ig, discarding those with common prefixes automatically and inspecting the rest by hand, I obtained a total of 66.