That's going to be a problem.
The file layout and/or folder structure for some apps is different, so Mail, for example, on the Lion partition won't be able to deal with a Snow Leopard setup -- it will try to convert the setup to Lion, and then Mail on Snow Leopard will be mystified.
Many apps will be fine, but you'll have to be careful in the future to update both. At some point, you may not be able to get compatible updates that will run on both Snow Leopard and Lion, and be in a similar pickle as above.
Most folks who have dual-boot situations do so because of one or two apps and/or hardware that only works on Snow Leopard, so they put everything for Lion on their Lion partition, and only what's necessary for Snow Leopard on that one.
I understand that you can run Snow Leopard as a Virtual Machine under Lion (or perhaps Mountain Lion). That might be a better option.
The entire drive has to erased and formatted GUID OS X Extended Journaled by Lion Disk Utility or Lion RecoveryHD's Disk Utility or via Internet Recovery to prepare it, the GUID, RecoveryHD and EFI for Lion compatability.
Once the drive is inside the machine and booting into Lion, then head to Disk Utility and create a second partition and give it a format OS X Extended Journaled.
Reboot the machine with the 10.6 disk (or USB thumb drive) holding the c or option/alt to boot from it and target the second internal partition to install OS X 10.6.
Quit and Reboot holding the option/alt key down to select the 10.6 partition and setup, then Software Update to 10.6.8.
You also can boot and erase/format the entire drive using the 10.6 disks, then Software update to 10.6.8, then create the second partition and use Carbon Copy Cloner to clone A to B, then boot from A and upgrade to Lion.
Keep the files you want to use in Snow Leopard in Snow Leopard partition.
Keep the files you want to use in Lion in the Lion partition.
Use a external drive to transfer files from Snow Leopard to Lion.
Cross compatability and/or a shared data partition will not work as Lion versions of programs will alter the Snow Leopard created files, so it's a one way street.
However some generic cross platform/operating system versions of files like jpg, mp3, .mov, .doc, .txt and so forth likely have no trouble crossing back and forth.
Apple is all forward and no backwards, once your files are altered by later OS X verisons and by their software, they are almost incompatible with earlier OS X versions.