How can I resize a partition with Disk Utility? I have 2 partitions, I reduced the size of one and want to expand the other to fill the now available space. 

How do I expand the Lion Partition into the empty grey space beneath Macintosh HD partition?
You can't change where each partition starts (i.e. where the top of it is in the partition diagram), only where it ends.  But in your case, since you have a free block as large as the partition you want to change, you can work around it (warning, this is untested under Lion, so make sure you have a good backup first):


Create a new volume in the blank space between your two existing partitions. Give it a distinctive name (you won't want to mix it up with either of your current partitions).
Boot from the Lion restore partition (boot with the option key held down, and select Recovery HD from the icon list and then click on the arrow under it).
Run Disk Utility.
Select one of the volumes in the sidebar, then the Restore tab on the right.
Drag Lion Partition into the Source field, and the new blank partition into the Destination field. Do not get them backwards!
Click Restore, and wait for it to clone the partition's contents.
Quit Disk Utility, then choose Startup Disk from the Apple menu.
Select the new partition (it may be difficult to tell it from the original, as they're now both named "Lion Partition").
Reboot, and verify that everything is working right before proceeding.
Run Disk Utility, delete the original Lion Partition and expand the new one into the newly freed space.