Not quite sure exactly what Drum Maker is after, but I'd allow at least 500mm space for the operator in front of the handles, and enough space on the left to slide the tailstock off without twisting my back. About 200mm on my machine.
I prefer to have much more space at the headstock end so I can get at the change gears and belts comfortably. It's also handy to have plenty of room to overhang rod out through the spindle. Some jobs, like threading the end of a pipe, need a few metres and space for a trestle support. I have about a metre.
I mounted my lathe sideways with the tailstock at the wall end and overhanging a storage box, and back to back with my mill. This gives about 350mm rear squeeze access to both machines: jolly helpful if anything falls behind or I need to get at the VFD, or motor or the mill's rear oiling point. Now I'm less supple, I'm finding it harder to get out of a 350mm space. Nearly got stuck last time I went in – not strong enough for the necessary contortions. Reminded me of Beatrix Kiddo punching her way out of a coffin after being buried alive. I'm not fit enough to be a Deadly Viper!
Sideways turned out to be better than having the lathe against the wall. It was an accident! I hadn't quite cleared enough space for my engine crane to swivel the lathe into position against the wall as planned, so I plonked it down at 90° instead. Worked out so well I won't change it.
For H&S reasons it's not good to work crammed up against machinery, especially if other people areabout. Last time I visited a machine room there was enough space around the machines to drive a fork-lift truck around them. However, needs must in a small shed!
Dave