Is it possible to run 10.6 and 10.7 side-by-side and share a user profile? I would like to know if it possible to share an user profile if you have both 10.6 and 10.7 installed on the same machine (different partitions).

So far my experience was not a good one but maybe I did something wrong.

I am interested mostly in sharing iTunes library, Outlook 2011 database and other user setting.
You can specify the same home folder, but I'd suggest leaving them separate since you'd potentially have incompatible preference, cache, and other "Library" files between the two versions of OS X.

Perhaps symlink the corresponding preferences for the apps that you want to share data.

iTunes Library is easily shared, just hold the Option key when launching iTunes the first time to specify the library to open (it will remember it subsequently).

Since Office 2011 wants to use the Microsoft User Data folder within ~/Documents, you'll likely have to symlink this folder from one of the profiles.