I'm in Zone 6. We moved into the house just over two years ago, and there
was a lilac in the garden. It looks very young. It's really only one stem
going upwards with some offshooting branches. It is now about 6 feet tall,
but has not flowered as of yet. Do lilacs only flower after a certain age?

Get the soil tested -- if it is too acidic you may need to adjust the pH.
Also, there should be more than just a single stem -- Lilacs are shrubs.
Are you certain this is a Lilac? You may want to post a few pics in the
binaries group (close ups on leaves and stems). Lilacs bloom on new
growth -- anything look new on it from last season?

I have one Lilac that's about 3 feet tall, has a bunch of stems, and it
blooms every year (3rd season in the ground this year). I have another that
I did not get out of the pot last year plus it's about 1/3rd the size of the
other and not only did it survive the winter but it has more blooms than the
one that IS in the ground!

James