A few shots of the lilac in question.

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"How big a pot should it be in"

The pot it is in right now seems to be working, so you could keep it there.

"How much root pruning should I do? Should that be done at the same time as the foliage?"

DON'T root prune it at the same time you prune the top. You will be pruning the top after bloom. You will prune the roots during dormancy. Read this post for good advice regarding root pruning: Trees in Containers

"Is the plant still cold-hardy in a container?"

Maybe not. It may be too cold for the roots, probably at least 1 zone (maybe colder) than your actual hardiness zone. Your options could be to put the container in a protected place (cool, unheated garage/shop/basement/etc.); burying the pot in the ground; mulching the pot very heavily; or putting the pot in a large cache pot with insulation around the inner pot.

Good luck. I'm sure someone else will chime in with more/better advice.

Cheers!

Height control is most efficiently accomplished by pruning a foot or so lower than the maximum height desired. This is best done immediately following flowering. At this time, you should remove all but 2 or 3 basal suckers which will be allowed to replace the stems you'll be removing in your yearly maintenance pruning, which we'll get to in a moment.

Prune the roots/repot in early spring before bud movement.

Now we arrive at maintenance pruning, which is necessary for continued healthy lilacs that will continue to grow with good vitality. In a container, your plant should be limited to around 6 stems. This mid-winter, remove the largest stems and basal suckers so that only 6 young and vigorous stems plus the 2-3 basal suckers you left remain. Stems should be attractively oriented to each other. Next year, the suckers will have grown and you should remove the 2 largest stems again. This puts you on a 3 year rotation of replacing mature wood, keeping the plant juvenile (ontogenetically, not chronologically) and vigorous. Remove all small twiggy growth annually. Damaged or diseased wood should be removed as soon as it is noticed.

Deadheading or removing spent flower heads may marginally increase the number of flowers the following season, but the practice is actually more nearly a cosmetic measure than a necessity. A healthy lilac will flower in most years whether deadheading is done or not.

Always use a fast draining soil (I suspect yours is in a water retentive mix by the appearance of the plant), keep it a little on the dry side, and stay clear of high N fertilizers. Something in the way of a 1-1-2 ratio fertilizer would be best in containers. A soil test would determine what's appropriate in the ground, but generally a 1-2-1 or 1-2-2 ratio is recommended.

I do think your plant would benefit from potting up now (as opposed to repotting - lots of suckers all around the perimeter of the soil mass, it appears) and from following the care guidelines I suggested, beginning this winter.

Take care.

Al

If placed in a cool garage (heated, around 50 degrees) over the winter, will the plant require light? (If so, can I just move it inside the house near a window, or does it need a real winter to stay healthy?)

"Potting up" means remove existing soil, clean up suckers and repot with the well-draining soil? I'm not sure what potting up is vs repotting.

Thanks for all the advice so far.

Not in a heated garage. No heat! Lilacs are a hardy deciduous species that do have a chill requirement. While I am not certain about the amount of chill required for a lilac, plants with a chill requirement generally must spend hundreds of hours in the 40's or below to satisfy their needs.

No light required; the plant has no leaves, and photosynthesis is not taking place.

"Potting up" means to keep the existing rootball and most of the existing soil INTACT, and placing the rootball in a larger container, an inch or two larger on the sides. Fill the sides in with new soil. What I do if I "pot up" a badly rootbound plant; with a knife, I make 4-6 vertical cuts around the rootball, about an inch or so deep, then I remove any obviously dead or completely severed roots, then I "pot up". When you actually do your root pruning next year, you will treat the roots a lot more drastically/aggressively than that.

Maybe Al will chime in again with some better advice/ideas for potting up, and winter care.

Good luck!

Most Syringa are hardy to zone 3-4, so you shouldn't need to worry about the plants ability to tolerate a winter in your zone (check what I said to be sure, though). Just bury the container out of the wind/sun and it will be much better off than if you tried to nurture it. It NEEDS a lengthy period of chill to release it from dormancy and to grow with something near its potential genetic vigor in the subsequent growth period. Mother Nature knows best. ;o)

Dormant or quiescent deciduous plants require no light during their winter rest, BTW.

The link RG offered above goes into more detail about repotting vs potting up. The difference is major, but you should consider the repotting option unavailable to you at this time because of where the plant is in the growth cycle (in leaf).

Al