If you use heel cuttings from second-year growth, you'll get better results. Don't use fertiliser on cuttings or very young seedlings. Just dip the cut end into some pure honey, then dibble a hole into the potting mix with your finger or a pencil, insert the cutting, tamp soil around it gently with the finger-tips, water in and sit back and wait. If you're concerned about over-watering, make a little tent by bending some coat-hanger wire. Insert the ends into the pot (right at the perimeter), then cover the whole thing (pot and all) with some clear plastic. This will create a mini-climate of humidity and heat which will give the cutting a good head start. Once the cutting has grown and is touching the plastic, the cloche can be removed. Give it a week or two to adjust, then plant where you want it. Use the same technique for other woody shrubs like rosemary, too.

I have saved seed from my Munstead lavender & obtained a number of seedlings that I eventually plant outdoors. I was experimenting the first time, but have had success since then as well. I use standard soilless mix, usually in a square 4" pot (or pots), scattering a pinch of seed across the surface of the pre-moistened mix, then I lift the little pot and, using 2 hands, carefully shake it sharply and rapidly back & forth 6-8 times in order to settle the seeds into the mix, then very lightly pat the surface. Next I bottom-water the pot(s) by placing them in a shallow container of Maxi-Crop solution (one can certainly use just plain water, but I like this seaweed derivative). Once the soil is just moist, I put the pot(s) into a container that I can cover with a clear dome or lid and set it under lights (though you would not have to have light until the seeds germinate). Be sure to remove the cover for a while if condensation forms under the lid or you can have a mold problem and damping-off. I cannot recall offhand how quickly tiny seedlings appeared, but I do recall that I was rather happily surprised the first time I tried it, so I'd guess it was not more than 7-10 days, possibly less. I am not the most patient person when waiting for seeds to show up! Once the seedlings form their true leaves, I allow the soil to get a bit on the dry side (of course, one never should over-water lavender anyway!!), then knock the soil/root ball out and gently separate the individual seedlings, planting them into into cell packs. From that point on, they will benefit greatly from 16-hour days. Once they have shown good growth there for a few weeks, I pot them on, each into its own pot (2 1/2 - 3" square ones) of Pro-Mix organic mix to which I add some of my worm compost. They remain happy in these pots until they reach a nice size for planting out into the ground. I also pinch them back by about 1/3 when potting on, to encourage them to branch out. Hope this helps. Nothing like a row of lavender in the yard to make people & bees very happy!

Kalanchoe marnieriana. If these aerial roots hit the soil, they will root - so beware of them hooking into a neighboring pot! LOL Yes, speaking from experience. You can actually cut them off with no damage to the plant. Or you can let it get bushy like this one. I "think" that when planted in the ground those aerial roots eventually help prop up the plant as it spreads. And they really have pretty flowers, too.

It was a long time ago... but it was probably in late spring or summer when the plant was in active growth. The problem with rooting a cutting now would be getting it in the ground in time for it to get established before freeze-up. I’m not sure when that would be in Chicago.... But if whoever gave the OP the cutting might be able to give another one in spring if this one failed, I’d be inclined to give it a try and plant the rooted cutting either in a sheltered area close to the house to give it as much time as possible in unfrozen ground - or plant it in a large pot and store it in the garage for the winter. DH grows rosemary in a pot that he stores in the garage for the winter - rosemary would never survive outdoors in winter here but always survives in the garage. While I haven’t tried it, I’d bet lavender would do the same. Our garage is uninsulated and unheated. The pots are stored in the middle section of the garage. There are windows high up on the outer wall so there is light but it’s not particularly well-lit. What survives in there can be variable. The hardy begonia gdinie gave me last year didn’t survive and neither did a butterfly bush seedling. But rosemary did, as did garlic, and carrot and green onion seedlings. Leeks can be harvested during the winter from the pots in the garage. The OP probably has nothing to lose by trying... The alternative would be to try to grow it in a pot indoors. If the OP has a grow-light set-up it might work, but might not too....! Flip a coin! (Is it possible to take a cutting from the cutting and try it two different ways...?)