If you are asking the question:
"Can my phone get LTE speeds in the Caribbean?" then the answer is "Yes, as long as you get a SIM from a provider that has LTE, because the phone is unlocked and has the appropriate radios." However, I don't think you are asking that. You are asking, "Since I have a Simple Choice plan with T-Mobile and the countries I am travelling to are covered in the international coverage included in that plan, will I get LTE?" The answer to that is no, or at least probably not. The Simple Choice plan gives you unlimited data and text as well as $0.25 a minute calling in all of the covered countries, but it's not LTE. It's only guaranteed to be 2G, but depending on the country you may get speeds somewhat approaching 3G. But it won't be LTE, unless the roaming agreements between TMobile USA and these international carriers have greatly changed since I used them last year. I have been to Colombia, Jamaica, Costa Rica, and Australia in the last year and in the first three countries it's been 2G, maybe slightly faster. In Australia it was definitely 3G. But, it's usable, and it's included in your plan, no need to mess with new prepaid SIMs or anything like that. Your plane will land, and as soon as you turn on your phone you'll get a text from tmobile welcoming you to the country and confirming that you are in a covered location. Make sure to turn on data roaming.
EDIT: Ugh...sorry, didn't see that you were only asking about Mexico for LTE. Disregard my unnecessary post.