I've never had mites myself, but some of the things I've heard people say work is A. changing the substrate and B. putting the T in a deli-cup with a moist paper-towel. The mites are supposed to all migrate to the paper towel as it's better for them than the T.
The reason I ask is that phorid flies are a lot more common than mites and some have mistaken them for mites. If they are phorid flies which I suspect they are by it being a lividum and probably kept moist the best thing to do is let them dry up as they will dry up and die long before the spider. If they are small gnat looking things that can fly but prefer to hop or scoot around then they are phorid flies. If they are climbing all over the T then they are probably mites and the before mentioned wet paper towel trick works well.
I don't know the humdity requirements for H. Lividum (Never had one)
But if they can live in bone dry conditions, change the substrate and let it stay dry with just a water dish. The mites will go to the water dish and drown. (Normally I'd say use a paper towel as substrate for mites just because it's easy to change (Less problem of mites down the road) but since H. Lividum are burrow-crazy, it probably isn't the best way to do it.
Predatory mites are THE way to go. These bennificial mites feed on other mites, as well as other pest critters in the cage, including fungus gnat eggs. When they've eaten all the available prey, they die off, leaving the T. and it's cage pest-free. I can't say enough good stuff about them. I order a couple pints (them come packed in moist vermiculite) every year or so and dose all my invert cages (especially the moist ones) with a spoonful or two. Works like a charm!
You can order Hypoaspis sp. mites (the predatories) from biconet.com look for them under the section "fungus gnat control". You'll be glad you did!