Hello.
I have never done this. It looks like I can install a new Mac OS X in a VM (Fusion Pro v6.0.3) from my old Mac Mini's HDD if I use "Install OS X from recovery partition". Mac Mini was from mid-2011 that has the updated Mac OS X 10.7.5. Anyways, here is what I did:
1. Created a new VM through its more options.
2. Picked "Install OS X from the recovery partition."
3. Created a new shared Mac Mini's Mac OS X 10.7.vmwarevm file that took a few minutes.
4. Booted up VM.
5. Picked English language.
6. I got Mac OS X Utilities menu with options.
7. I assumed to pick to "Reinstall Mac OS X" to install a new copy.
8. It said I needed to verify my machine's eligibility with Apple online to download and install.
9. I agreed with its license and picked my Mac HD with 42.55 GB free.
10. I got "This Apple ID has not purchased 'OS X Lion'". I don't re(call/member) ever buying Mac OS X 10.7 (Lion).
I thought I could install Mac OS X 10.7 Lion from my Mac Mini's internal recovery partition. Am I not allowed to use it for VMs? 
Thank you in advance. 