We started our development of the above mentioned LCR Plotting Routines on a RPI, then ported to a PC under Windows 10.
Got this working, and we are not good at software, firmware and coding, so you should be able to do this without too much effort!!
BTW believe the RS232 Standard is the most Non-Standard Standard ever, with all the various levels, connectors, cables and such
Good luck with your revived 34401A
Best