I would like to plant some Lilac but may be cursed with Missouri clay. Will Lilac generally do OK if planted in clay-rich soil? What is a good way to start a new planting?
Depends on the variety of lilac to an extent - the smaller, dwarf bush types are more finicky about soil conditions, but any variety from Syringa vulgaris (Purple Sensation or Madame Lemoine for instance, many others) will be less so.
Lilacs do not like wet feet, particularly in winter, so if you have heavy soil, its best to find a spot which slopes a little and plant the lilacs above the bottom of the slope, so that water can drain down away from the lilac roots. The soil should be well cultivated and improved before planting by adding plenty of humus rich material, such as composted manures and the like. Ph of the soil might be an issue, as you have clay, and its probably worth testing that - they're happiest in a neutral ph, or slightly alkaline, slightly acid, so a ph between 6.5 to 7.5 is ideal. They prefer full sun, but will grow well with less than half a day's shade.
I have grown Syringa vulgaris in Dallas, TX in amended clay soil with good success. The previous response was right, it does best grown on a large mound or higher on a slope so that the water drains away from the roots. If you do elevate it sufficiently, then the amended clay will be of a benefit to you in the hotter part of the summer because it stays moist longer and is full of nutrients. Dig the hole at least 2 feet deep and wide and amend the soil that you dig from the hole with whatever you need to get the pH right. My soil is 7.2 and I add gypsum, sulphur, manure and 2 parts soil to one part planting mix and peat moss to help break up the clay. You can use pine needles and shredded pine bark. You'll have a little more mass to put back in the hole, so mound the dirt when putting back in the hole and plant the lilac so it's planting depth is raised to meet the mound. I would suggest to get a soil testing kit online to test your soil. While they will survive in a wider pH range, they will flourish between 6.5-7.0. The lower pH also helps unlock nutrients that are bound in the soil and not available to the plant at higher pH above 7.0. You may have better luck with the Bloomerang reblooming lilacs, as they do much better in clay and actually thrive in it here if you keep it watered regularly. I am not sure how hot it can get in Missouri, but in Texas, I have to provide shade because it can get over 100 here for 2 months. I plant mine on the east side of the house so the roof provides evening shade and saves it from burning in July. I even have Peonies around the base. Good luck with it!