Bojans,
In a nutshell:
Static phase converters are basically a box full of balancing capacitors. They are "static" because they don't require an idler motor. However, they only allow the motor to develop 2/3rds rated power. This can be problematic for a hydraulic pump installation. One static converter is required for each motor.
Rotary phase converters add a motor to the box of capacitors and provide true three-phase power. You can use the power they provide just as if it was a 3-phase service and run multiple machines. They can be simply a motor, or a motor with a box of balancing capacitors. Properly balanced, they can provide power just as good as what the power company supplies. They're easy to build and plans are readily available.
A third option is the relatively recent invention of "digital phase converters". These use electronic methods to convert 1-phase AC to DC, then chop it up into 3-phase AC. The power they supply is actually more stable than what comes in off the lines and like with a rotary converter, you can use it as a 3-phase service. They're expensive though.
Finally, there's the VFD. This is like a digital phase converter, but with the added ability to change the frequency of the output. However, these must DIRECTLY control the motor, with no switches between the VFD and the motor. This means the control circuitry of your lift would need to be re-wired to put the VFD in direct control instead of the motor starter.
I would build a simple rotary phase converter to operate that lift.