I have a few lilacs on my property, but this one in particular is next to my house. When and how should I prune it? Ideally, I would like it to be about two feet less in diameter, but I’m worried that would cut off all the greenery.
If it is winter in your area this is absolutely the WRONG time to prune. Lilacs should be pruned immediately after blooming. By pruning at this time you will not get flowers this coming spring. If you prune this winter you not only sacrifice this coming spring blooms, but will encourage it to shoot up really fast in spring. You will then end up with a shrub bigger than before pruning.
Prune no more than 1/3 of the shrub. You can prune the whole thing by 1/3 or take 1/3 of the branches this year, take out another 1/3 the following year and the last 1/3 in three years. If you continue to do this pattern, you can help maintain size of the bush. Or you can prune 1/3 of the entire shrub right after blooming. This will reduce the overall size of the shrub if this is your reasoning for pruning in the first place.
Whatever 1/3 process you choose, make sure you do it right after it blooms. Lilacs sets buds (next years blooms) within a month of blooming. So anytime later you loose blooms the following year.
The right time to prune is over winter (November to March in the UK) when the tree is dormant. If you are in a harsher climate than the UK, don't prune when the wood is actually frozen.
Don't worry too much about "cutting off all the greenery". The easiest way to prune a totally overgrown lilac (so long as you don't want instant results) is to just saw through the main trunk two feet above ground level, and wait two or three years for a "new tree" to develop. Yours doesn't look bad enough to need that sort of treatment, though.
Take out complete branches to reduce the volume of growth, and then trim back what is left to the size you want. You should get new growth coming from the center of the bush the following year. The following winter, prune back more of the old wood and trim the new growth to the size and shape you want. Repeat that for a few years and you will have a "new" smaller sized tree, and still have flowers every year while you were reshaping it.
It's a nice specimen of a lilac. Very attractive in bloom. But that is only a few weeks in the year - all year round you need access to that garage and light through the window. My argument is this is the wrong place for a lilac, which is much better in a hedgerow or more open ground where it can grow to full majestic maturity without interference.
The reasoning is that any attempt to prune back the top should ideally be matched by pruning the root. Without this there will be a massive response by the top half as it sends out numerous suckers and whippy branches that need frequent pruning back to keep them under control and unless you are very careful you will lose that fine shape and quite probably prune off a lot of potential flowers. Root pruning in that location will be really hard; I imagine the roots have filled the patch under the window in the walled well and have pushed under the cement cobbles by the driveway.
Thererfore my radical suggestion is to get it out of there and replace with something that can be easily boxed in and will behave, perhaps with a Forsythia which when fairly mature can stand annual frequent clipping to shape and still produce flowers. You say you have lilacs elsewhere in the yard probably in more open space and that is where they belong.