How permanente a solution do you want
 

Personally, I would want to know what's going on and is it going to continue.
Most foundation issues, including settling or heaving concrete, derive from poor backfilling/compacting when the house was built. Thus, long term, if you take quick cosmetic measures, it's going to occur again...sometime.
Your Option #3 (and most expendive) would be getting a foundation company in getting it taken care of properly.
However, personally, we have a close friend who had the same situation in Rio Ponderosa, I put a 60 tooth carbide blade on my 5-1/2" trim saw, took the screen door down, took the door sweep off the bottom, and trimmed a half inch off the bottom. Then, attached a new door sweep and adjusted it when door was installed.
Keep in mind... when the split becomes a hazzard, you'll need to rent a small electric jack hammer and remove the high side of the split, down a half inch or so and at least 6" out from the split, clean it out and use an epoxy concrete patch and level out. Once cured, clean the whole lanai concrete and paint

Mud jacking for long term solution

Cut the bottom of the door

I have a large oak tree in my front yard, and the roots are everywhere, and I have already paid to have part of the side walk ground down due to the roots displacing the walk way, and noticed my drive way lifted almost and inch on one side. Can I have the oak tree cut down? thanks

already too high
mudjacking won'thelp - no diy solution other than grinding imho

You need to contact a licensed arborist to make a determination of the tree and the damage. They can then file the paperwork to have the tree removed legally. One company that I understand that can do this is Tree Frog, give them a call and they will tell you your options.

thank you

Are there pictures or did I miss them.
 

I didn’t see any pics. There is no way responses can be viable without the responder seeing a picture.

[QUOTE=BEETHOVENMIKEY;2018324]Personally, I would want to know what's going on and is it going to continue.
Most foundation issues, including settling or heaving concrete, derive from poor backfilling/compacting when the house was built. no/one can know definitivly the reason for failure dia grindinggenerally structural but cab be cosmeticci, it's not necessarilygoing to occur again...sometime.
Your Option #3 (and most expensive)(expensive') would be getting a conc repair contractors/pecialist to a care ofit properlygruound
However, personally, we have a close friend who had the same situation in Rio Ponderosa, I put a 60 tooth carbide blade on my 5-1/2" trim saw, took the screen door down, took the door sweep off the bottom, and trimmed a half inch off the bottom. Then, attached a new door sweep and adjusted it when door was installed.
Keep in mind... when the split becomes a hazard, you'll need to rent a small electric jack hammer (you're kidding right? - hammer drill & bushing tool !!!and remove the high side of the split, down a half inch or so and at least 6" out from the split, clean it out and use a polymer modified concrete patching material & finish!. Once cured, clean lanai more thing there's no paint that's resistant to wear from pedestrian traffic IF there were, we wouldn't have to repaint porches!!!!!!

Contact Villages warrantee department. They may be able to get the original contractor to come fix their poor work.

It's a 10-year-old villa.

It's worth a call to warranty. T&D warrants their concrete work for 10 years.

I vote for reducing the door size and I would do it with an offset handheld grinder and a super abrasive wheel(like a 24-32 grit). After you grind the bottom say 1/4" move the door sweep up by drilling new holes. I would also dig around the outside of the part of your lanai that is elevating and look for the cause of the concrete shift. Grinding the concrete would be very obvious and in my opinion look quite bad.