50 amp, 240 volt hookup without equipment ground

I wouldn't do it without a ground. The ground wire should be there someplace, look close at the wiring where it comes out of the shielding, the ground wire could be there but just cut off when the shielding/insulation around the wires were cut. Another option might be (but don;t quote me) is if the house has copper water pipes and are connected to a metal pipe running outside the house under ground, you might be able to run a wire to this for an independent ground.