Yes, they use the same drives, so physically it is possible, although you'll need to swap the mounting screws, because the screws in those machines are different.
And as far as the software on the drives, it's generally possible to boot up into another Intel Mac's hard drive, as long as the memory and other hardware elements are roughly equivalent. Due to Apple controlling both the hardware and software that goes into its machines, Macs are far better about this type of thing than PCs. If it kernel panics the first time, power off, and power on again. A PRAM reset and a PMU/SMC reset might also help, especially if the computer takes a long time to find the boot device after the swap (blinking folder or a blank screen for a minute before the Apple icon appears, etc.)
Another option is to put a fresh install of Lion on the A1278, and use the Migration Assistant in the setup wizard to point to your A1181 (without swapping drives) and seamlessly copy all your data over. I don't know what variation of the Lion installer you have, but the one I've got allows you to go into Disk Utility, wipe the drive, and then close Disk Utility and do a fresh install, i.e. a non-upgrade.