We had the same problem several years ago with lilacs that were probably fifty years old and had never been pruned. You are correct in pruning out about 1/3 of the clump making sure what you prune is the oldest wood. Be sure what you prune looks like a tree branch, the roughest looking rather than smooth wood. Many say two inch sized stems should be pruned out. We also trimmed out the skinny suckers at the base of the shrub.
After flowering is done for the season you can shape the lilacs. Ours were maybe fifteen feet tall and we shortened the leggy branches and generally rounded the entire shrub to the shape and size we wanted. It is difficult to prune too much, but that will not really hurt the plant.
The next year there were blooms but not really a big amount. The next year we pruned a few more of the old, woody branches but not a third, maybe just two or three branches. And we did not shape the lilac that year. Then by the second year after thinning , shaping and pruning, the blooms were larger, lasted longer and the numbers were way up. Since then some nominal pruning to keep the shape was all that was needed. Always wait until the blooms are gone before pruning branches. Buds for next year will form very soon after the flowers fade so if you wait too long you will be cutting off next years blooms.