I have 3 phase Y 208 at my office. Purchased a lift that has a pump motor on it that requires 220 sigle phase. Any two legs of three phase are 120 degrees out of phase, I have seen wiring for welders wired this way, but a - motor probably requires 180 degrees phase difference? Step up transformer or other solution?

Just hook it up to 208V. It will work fine.

What type of engineer are you?

2-wire motors are wired line-line. There is no phase difference between only two wires. The concern is that you actually have enough voltage to run your motor, the worst case is you will need to use a buck-boost transformer. Is your motor really 220V and not 230V?

Have you asked the manufacturer or the pump motor manufacturer??
This is not to be taken for an answer to you application but some background for the answer you should get from the manufacture.
If in fact it is a 220v motor od it NEMA rated? If so antivipate that it is able to operate satisfactory a +-10% of that which would be 220 x.90=198v. I did not say that the device was capable to operate at down to 198v but there's a good chance that it would be an accurate answer.
Remember one thing. If a motor is rated at 10HP at 220v it will draw a specific amount of amps to product 10HP. In doing so there will be losses in heat. Now reduce that voltage to 198v. To produce the same 10HP the motor would have to draw more amps to produce that same 10HP. More amps = more heating.
It is common that whem a motor is applied it never is required to produce its nameplate HP anyway.