According to the manual (which i sent you a link to in a PM by the way) it says that the single speed ones are 3hp and the dual speed ones are 3hp/1.5hp depending on whether low/high speed is selected, although there were a range of motors fitted depending on the location the lathe was sold. It would probably be best to swing open the motor mounting plate at the rear of the base and take a look at the motor data plate to be sure.
One thing you should be aware of though, if it is an original motor in there, then they are wired for 415VAC 3 phase star configuration and are not reconfigurable for 240VAC 3 phase delta operation as you would get out of your inverter. (At least mine wasnt reconfigurable for delta operation)
I run mine from a 240VAC inverter, but I stripped the motor down, and did some modifications to the windings to allow it to run in 240VAC delta configuration instead of 415VAC star. (Basically brought out the internal star point to external connections)
I have no idea how well the lathe would run if you attempted to run a 415VAC star configuration motor on a 240VAC delta inverter output. Perhaps someone else could chime in here.
If the answer is that it wont run well, then to run via an inverter, your two options are to modify the motor to bring out the star point to allow delta operation (not easy), or replace the motor with a 3 phase motor that can be configured for 240V delta.
Another couple of things to bear in mind while were talking about electrics
1. The suds pump is 3 phase aswell, although mine was a dual voltage motor which is easily re-configured to run from a 240VAC 3 phase supply as you would get from an inverter. I run both the lathe motor and suds pump motor from a single inverter without any issues (I did leave the suds pump wired in via the suds pump switch, so I can choose to start the lathe with suds on or suds off by using the switch…. I try to avoid switching the suds pump on while the inverter is running the main motor, as all the reading material would suggest that turning loads on/off a loaded inverter could damage the inverter)
2. If the lathe is fitted with a light, then the light will probably be fed from the Phase 1 of the 3 phase supply. There is a transformer in the lamp switch box bolted to the back of the headstock which contains a transformer which is probably expecting to see 415VAC single phase input. The transformer converts the voltage to a low voltage (cant remember off hand but 28V sounds familiar). The wiring on the transformer can be altered if the input voltage is not 415VAC to ensure that the bulb voltage is correct. On my lathe, I fitted a 3 pin UK plug and lead to the lamp and powered directly from a mains socket. I reconfigured the transformer inside the lamp housing to accept 240VAC input and thus the lamp is now independent of the inverter input.
3. If you are running from an inverter it is probably worth re-wiring and bypassing the control panel start/stop buttons on the front of the lathe. You don't want any switchgear between the inverter and the motors. I start/stop the lathe from the inverter controls. Its not as fiddly as you might imagine as your lathe has a clutch so you can start the motor from the inverter and then start/stop the chuck using the mechanical clutch, then when your work is done, stop the lathe from the inverter.
Some things to think about anyway. If you're not up to scratch on 3 phase electrics, I would get an industrial sparky to drop in to take a look at your setup.