Pruning an old Lilac bush to get flowers
Some reasons lilacs do not bloom are: too much shade, they grow best in full sun; immaturity - many lilacs do not flower for five to seven years;
overly rich soil or too much nitrogen fertilizer. Soil rich in nitrogen will promote leafy growth at the expense of flowers. Improper pruning - pruning in summer, fall or winter pruning sacrifices flowers for next year. Prune lilacs immediately after flowering in the spring.
To rejuvenate your lilac you may want to do some renovation pruning. The plant will lose its looks for a few years and is done in early spring. If this is too drastic, take a look at the attached link for more information and yearly pruning tips that includes thinning and deadheading usually done after flowering https://www.finegardening.com/article/pruning-lilacs