I don’t live in Texas so I have no first hand knowledge, but I’ve always thought that Homestead Exemption applies only to where you reside. I can’t get the exemption on my rental properties, because they aren’t my primary residence. Now you mention lots and I read,no structure erected on them or otherwise unimproved. If they are adjacent to your home, and therefore can be joined together to make one property, then homesteading might be possible, but that brings up the matter of ownership of your primary residence.
Congrats on paying off your home, but now is the time to get the home in your name, and therefore homestead exemption on that property. As the will has been probated (the word you struggled with LOL), who now is the owner of record of the property. In the will, did it state that ownership of your particular property is now transferred to you? Was there a “right of survivorship” set up with your parents to their other properties? To me, I would concentrate on handling this matter first, versus homestead exemption on lots.
Like I said, I probably didn’t help at all….