What's the problem with your LSJ? If the block and head is in overall good shape, just rebuild. If you have a rod through your block, find a gen 3 (LHU) block and use new LSJ rods/pistons internals and your LSJ head. Block good but head toast? Contact vendors like ZZP, CatV, etc and see if they have a head to sell you. I'm pretty sure that finding a replacement crank would be the most difficult, so if your crank is good that's a great start IMO.
It really depends on how handy you are, and what your budget is. For about $600 I refreshed my LSJ bottom end (rod bearings, main bearings, piston rings, main seals, timing chain guides/tensioner/chain, BradBUILT balance shaft delete, head gasket, main studs, head studs, head decked but not the block, head inspected/valve seals, etc).