Hi MrArun - I use imovie HD 6 exclusively, both on a recent iMac running OS 10.6.8, and on a Macbook Air running Lion.
And note this: on the MBAir as an experiment, I simply copied and pasted iMovie 6.0.3 from my old PPC G5's Applications folder into the MB Air's Applications folder - it works perfectly, and it had no effect on the already installed iMovie 11.
Matthew is quite right that some plugins will no longer work, but the excellent GeeThree plugins do have Lion-optimised versions.
I used the Migration Assistant when I got a new Mac, and it brought over Imovie 6 with no problems. I have heard it is difficult to install iMovie 6 from the DVD, because the installer program (but not iMovie 6 itself) needs Rosetta. So either use Migration Assistant or use the method described by Catspaw.