They're not standard massages.I think Lomi Lomi is a Hawaiian massage and tantra is a sexual type of massage.
By legitimate massage do you mean legal?If you do then i'm pretty sure that Lomi Lomi would be legal everywhere but "Tantric" massage could be legal or illegal depending on state or country as it might come under Prostitution.
LOMI LOMI is not anything to do with anything sexual but i guess the creators of it & massagers would consider that it has a "spiritual" element so it would be a good idea to check if it would match your spiritual beliefs(or lack of ) before deciding to book for this kind of massage.For example if your a Christian,this type of massage might be in contradiction with your beliefs because it does have quite a strong "spiritual" element with Lomi Lomi practitioners believing that the Creator is an "universal energy" that flows more freely with receiving this type of massage.This conflicts with what Christians(or muslims + Jews) believe God to be so if you have a religion and/or wish to avoid a type of massage that has a "spiritual' component/belief that that might be something to consider before booking this type of massage.
The "spiritual" aspect of Lomi Lomi is hard to avoid because often they will perhaps have crystals under the massage table,or might use "whooshing" sounds like the wind or start humming etc so its a bit "newagy".
Personally,i believe in Christian God now so for me Lomi Lomi massage wouldnt be suitable but i had it alot maybe about 3 years ago.So if you have a faith belief thats something to consider whether its compatible or not.
Also if you dont have a faith belief but are a skeptic who thinks all that crystals,"energy work" etc is B@llshit-then avoid this type of massage as it might contain that.
Also what needs to be considered before booking a Lomi Lomi massage is that often the person is completely naked with only a small piece of cloth covering the genital area so if thats something you dont wish/are uncomfortable with take that into consideration.
TANTRA massage as far as i'm aware is a sexual and sensual massage so if your just after a normal massage avoid that or you might receive an unwelcome surprise lol
If your just after your normal regular massage then avoid these two.They're not "legit" in that sense.
If its for pain then look for a Remedial massage.Your doctor might be able to point you in the direction of someone if you dont know how to find someone.Alternatively, if your looking for a massage for relaxation -eg:swedish,hot rocks,facials etc- then try a beauty salon or day spa or health/aerobics centre.Also if your in Australia you could try contacting the Australian Association of Massage Therapists and ask then who they could recommend based on your location & the type of massage your after-that way you cant really go wrong