I would check the specifications on the lathe, I believe the geared TS version is a 3Hp 3 phase motor, the TV (variable speed 2 speed) is 5Hp. If 3Hp, then you might consider a single phase input VFD, QMT sells the WJ200-22SF (about 1/2 the price of the Lenze listed, and a generic braking resistor is about $30 so might be around $320 total) that would work for a 3Hp motor. If it is a 5Hp three phase motor, for the most part you would need a 10Hp 3 phase VFD, which would be derated for single phase. A 7.5Hp VFD might work if you use a DC choke, but it gets pricey. I believe at that point it would be more practical to go with the TV model with the factory VFD if it runs on single phase, as the Lenze VFD, braking resistor and remote panel is probably pushing $1200. I would be more inclined to look at the Yaskawa 5HP single phase input VFD (BA0018FAA) and purchase a generic braking resistor (I can get you the specs) which will total around $700. Yaskawa is probably the most common factory installed VFD in this size machine, mill or lathe. In either case, it is not a direct bolt on and go, and there is a learning curve to the installation and programing.
https://www.steinerelectric.com/p/yaskawa-cimrvuba0018faa/545941
Normally for a lathe VFD conversion, it is not a simple process of connecting the VFD to the motor and running it with a remote VFD panel, that is often done with a mill. It is possible to selectively remove the high voltage wiring to the forward/reverse motor contactors, and then using these to drive the forward and reverse inputs on the VFD, but you cannot utilize many of the additional VFD capabilities. I have helped a few people do this on the 1340GT and 1440GT lathes. A full system rebuild, control board, switches and all the wiring can be time consuming and more costly, but more total control/features.
An RPC would be plug and play, maybe a consideration if you have other 3 phase machines. That being said, usually when one converts to a VFD, most people kick them selves for not doing it sooner. So different options to think about. This is definitely a bigger lathe with more capabilities then the typical smaller machines. Lots of good input from this forum, so good to get different opinions.
Mark