The rim really doesn't look that bad. The main risk would be from driving conditions that might push the jagged edge into the tire. Even if this were to happen, I doubt it would cause a blowout, though it might shorten the life of the tire.
I can't tell if there is any damage to the sidewall of the tire itself from your photo - I would poke around the surrounding portion of the tire and check for any deep gouges and punctures that might be cause for concern.
The next thing you should do is read the terms of your lease, and determine what your responsibility is. Sh*t happens, and this is factored in to the leasing company's calculations. You're not going to lose your license or get thrown in jail for this. I also doubt that this would be grounds for them to terminate the lease.
You can try to repair it yourself, but unless you are very skilled with this sort of thing, it's going to be obvious when you return the car and they do their inspection. They'll be more offended by the deception than the actual damage.
That being said, I doubt that anyone would expect the entire wheel to be replaced, and in fact it might end up costing you more if you go out and buy a new wheel rather than doing whatever the leasing company wants done.
If repairing it yourself is an option, the steps would be as follows:
- Tape off the surrounding part of the tire. This will let you know if you are inadvertently abrading the tire as you sand down the rim.
- Start with a file and remove the roughest portions of the damage.
- Start with a very rough grit sandpaper (perhaps 100 grit) and sand the area, working your way down to progressively finer grits. In the end, you'll want to be using extremely fine "automotive grade" sandpaper. This stuff is 2000-2500 grit. Always check the tape to make sure that you are not sanding the tire!
- Clean and dry the area.
- To me, the damage doesn't look deep enough to require any kind of filler. You'll only really be able to tell once you've sanded off the jags.
- I'm not sure if these rims are painted, or if this is the natural color of the alloy. If they are painted, you would need to find a matching paint and apply several thin coats, allowing them to cure and sanding between coats.
- There may be some sort of clear coat that you need to apply and sand as well.
- Use a good quality polishing compound and a microfiber cloth to polish the area until it shines.