irs setup is alot more work involved than live like said.
the toyota lsd diff's available are T series 6.7", F series 7.5" and G series 8".
the T are quite expensive due to demand and availability. even second hand can be around $600 for a std lsd head. the F are around but may need to look for a while. expect to pay $200-$300. G are common coz they're hilux but are overkill for a little ke25. the axles are bigger than the smaller size ford 9" axles! pay about the same for a G lsd head. for housings just go to pick-a-part as they're like $80 for a complete diff. the problem with bigger diff's is the width and will most likely require shortening and thats like another $500-$600 to get done at a shop on top of converting the mounts over.
the irs versions of these diffs can swap the internals into the live axle heads so even if you find a F series irs TA63 or irs ma70 supra or mx81 cressida G series lsd it can be swapped into a live axle head
this is what ive done on the hilux diff into ke70 and what im about to do with the F series lsd into my ke25 SR. F series lsd's are more commonly found in irs form in the ta63 or ma61 celica's or celica/supra's anyway and cost me $120 from a diff shop to get the gears and lsd swapped over..
hope that helps some.
you can also get a harder spring for the lsd to tighten it up and shim it for preload, or if its worn then get the clutches ground and add more shims to compensate.