Yes, the NT-06 Lite "fits" on the P5E-VM HDMI. That's what I'm using right now. You'll have to cut solder joints that get in the way of the mounting plate that you attach to the underside of the motherboard though, which isn't difficult at all.
Could you take apart your PC and show me what I have to do? lol, j/k I should be fine with getting it to fit. I do have some questions though....
What kind of temps are you getting with the NT-06?
you using a 120mm fan?
If so, which fan and is it mounted to the top or the bottom?
Which direction is the fan blowing?
How do you have the heatsink oriented?
Sorry for all the questions, but you are my only source of info. Any other pertinent info you can share with me would be appreciated. Thanks in advance.