Hello,
The shop I where I worked had three 15" Servo Shift LeBlonds. They were purchased new in the early 1970's. I think they were pretty good lathes especially when they were new. By the time I went to work there in the late 90's they had or were needing repairs. The basic lathe is fine and it is a nice machine to operate. The drive system seems to be too complicated for what it does. When I went to work there the only hydraulic shift lathe I had worked with was a Lehmann Hydratrol which worked good. The LeBlond system is very different.
I don't know much about phase converters so I really can't answer that question. The servo shift system works off the small hydraulic pump on the back of the headstock. On the ones we had it was controlled by the switch that is behind the servo dial or by the forward and reverse lever. The pump motor was controlled by a separate motor starter on the electrical panel. The pump fed a shifting block in the headstock that was connected to the shifting levers. This in ours was made of plastic and some developed leaks. At one time LeBlond would rebuild these.
The shifting system also relies on a magnetic brake that is behind the drive sheave on the headstock. It seemed like a real Rube Goldberg apparatus. When you turned the servo dial to a new speed nothing happened until you placed the forward/reverse lever in the brake position. The pump came on and a set of plastic gears moved a linkage that attached to the electric brake. This rocked the spindle back and forth so the gears could line up. When the shift was completed the pump turned off and you could engage the spindle.
The key to making this work was one more component. It was called the zero-speed switch. This was a mercury switch that was installed on the end of the motor shaft. It was required to make sure the motor wasn't running during all the shifting process. If that switch fails it can lead to damaged gears. If your lathe is older it may have had this switch bypassed. LeBlond stopped making the mercury switches and developed an electronic circuit to detect the speed of the motor. All of ours had been converted.
You could still get a lot of parts for the lathe as of about four years ago. I don't think the parts come from LeBlond but the company that sells them is very helpful with information and parts.
I hate to sound negative about the lathe. They were very good lathes. It just seemed they were overly complicated for the convenience of changing speeds. Once again, I can't answer the question about the converter. I believe it would work because the pump motor does not operate when the main motor is running and vice versa.
Good Luck,
Terry