Is it possible run LMS 3.2 on a Vmware ESX 4.0 platform?
ESX 4.0 isn't mentioned in the data sheet only ESX 3.0.1 and 3.5.0
No, VMWare 4.0 is not yet supported. IT will be evaluated for the next release of LMS due out next year. In the meantime, you will need to stick with 3.x.