Hi Clare,

Thank you for reaching out to the helpline. As a general rule for all lilacs, they should be pruned immediately after they’re done flowering in the spring. This is because lilacs set next year’s flower buds right after the current year’s flowers have faded. Pruning later in the summer or fall will result in cutting off many or all of next year’s flowers. 

You can also prune when the lilac goes dormant. This will allow you to see the branches better when the leave have fallen off. The best way to clean up an old/overgrown lilac is rejuvenation pruning. This is a three-year pruning program. As with many flowering shrubs use the rule of one thirds. In the first year remove one third of the largest, thickest stems as close to ground level as possible in late winter. Also remove any dead or unhealthy branches. The following year (again in late winter) prune out another third of the thickest stems. Repeat the process again in the third year. After that, you can resume maintenance pruning in the spring (just after the blooms fade) by shaping and cutting out any broken or diseased branches.

By not removing a very large amount of stem growth at one time, the lilac is able to maintain the energy to increase it's health and vigor. This type of pruning encourages a moderate amount of new young shoots to develop from the base of the shrub - rather than excessive sucker growth that can sometimes follow a major renovation pruning. This will result in a plant with young, healthy stems, producing many beautiful flowers.

I would not do any pruning in early fall when the tree has the opportunity to develop new growth this late in the season before frost. This may harm your already stressed lilac. 

Here are a few articles that I think you may find helpful:

Growing Lilacs

Pruning Lilacs

Please feel free to reach back out if you have any other questions. Happy Fall!