Other than that, I'd strongly suggest that you stop moving the poor thing so that it can establish itself happily into a permanent location.

Next season's flower buds, if they form at all, develop very soon after the spring blooming period. No pruning should be done after that time, whether you see buds or not.

Prune the lilac ONLY immediately after they flower (or in your case the time of year they should flower) which would be in April in the South. Don't prune now, since the flower buds are being formed in the summer (you'll see them become plumper and plumper at step tips).

Hopefully this last location you relocated the lilac to is in the coldest microclimate you have, such as being exposed to cold winter (NW) winds and NOT protected or warmed by nearby building foundations or pavement.

Truly the "soundest" lilacs for warm Southern gardens is cutleaf lilac (Syringa laciniata) or Manchurian lilac (Syringa patula), which is usually seen sold in the cultivar form of 'Miss Kim'. Note these really only do well as far south as zone 8.

Here's info more on 'Miss Kim' that I couldn't add in the one links box in the last posting.