This is really about engine cranes and moving heavy stuff. If a moderator wants to move this to some other thread or category that's perfectly OK with me.
With an engine crane quite often the difficulties come from the legs being in the way. Using a 2 ton rated crane I've moved as large as an old 1930's era South Bend 15. We removed the overhead drive first to reduce of center load and make it less top heavy. As this was one with the cast iron open leg set and overhead motor the engine crane worked well. If it had been a more modern cabinet base style we would likely have needed to set the lathe down on some cribbing, then done the alternate end layer by layer removal of cribbing using jacks and tommy bars. I have to play that game when moving my SB 10K.
As long as the center of mass can be kept safely within the footprint of the crane, weight and lift height are the only restriction. DON'T let the load getting swinging, stop as soon as it starts and get things calmed down. Particularly with the triangular leg configuration there is very little room for error before it can tip or flip.
Use good slings or chains, even if you spend an extra $50 on two or three real lifting slings, it's less than hiring a rigger. Cast a suspicious eye over all the slings you are going to use. There is no "iffy" rating here, it's either OK, or it's trash. If using rope, figure any knot will reduce the strength of the rope rating by at least 50%. That's one that's easy to overlook. If you can't figure out how to do the job, get help or hire a rigger. As Brian mentioned, they aren't cheap. If you drop a 3000 pound engine lathe down a basement stairwell that won't be cheap either.
If you have to lift high to clear a cabinet base, get the load as low as possible as soon as possible. Lower the load onto wood packing placed over the crane legs or a tranfer dolly if you can. Better to drive a trailer or truck under or out from under a suspended load than to move the crane with a high up load. Same if using a tractor, particularly with a boom pole. A high load greatly increases the chance of tipping. Only extend the boom as far as actually needed. If you need to move some distance, consider putting the load on dollies. Lift again at the far end of the move. I've never dropped a machine or gotten hurt doing a move, but I'd rather take half an hour longer and stack the odds in my favor. Whenever doing a heavy lift, know where everyone is, be sure everyone knows the plan, and know where the load will go if it all goes wrong. Don't be there. I assure you, you won't have time to get out of the way. Lucky, hurt, or dead are the options if you stand in the wrong place.
Engine cranes have quite small wheels which easily trip even on a small pebble. Sweeping well before using one helps. Putting rings cut from PVC pipe around the wheels helps too, the rings need to be taller than the mid point of the wheel. The wheel pushes the ring from the inside, the rings help push any debris out of the line of travel. Useful with shop vacuum wheels too.
Hope everyone stays safe and healthy in these weird days!
Stan