Welcome to WF!
Yes, your '99 TJ has one of the more "bulletproof" automatic transmissions going. The model # is a 32RH if you have the 4.0L engine, a 30RH if you have the 2.5L engine. Both are very reliable, simple, and generally problem free. I converted my '97 TJ from a 5-speed to the 32RH about two years ago, it's a superb transmission for hardcore offroading.
It requires you use either ATF+3 or (better) ATF+4 inside. Personally, I wouldn't trust Jiffy Lube to hold my wrenches while I did the job.
Likely it has not had its ATF changed so it's a good idea that you do at least a partial ATF change together with a new filter which is a very easy job.
If you want to tackle it yourself, it's not a bad job if you're handy with tools. Otherwise, I would go to a small INDEPENDENT transmission shop listed with your BBB and tell them you just want an ATF change with a new filter. Like Jiffy Lube whom I recommended you avoid, I would also avoid having the work done by any chain type transmission shop like Aamco. Chain shops like that have minimum sales quotas to satisfy the home office & are likely to find additional "work" they'll claim needs to be done which is usually just a way to unnecessarily jack up the price.