Yes, but you must upgrade to 10.7.4 or later or to Mountain Lion. You can redownload the Lion you purchased from the App Store for free.
I recommend:
How to Install Lion/Mountain Lion Successfully - You must have Snow Leopard 10.6.7 or 10.6.8 Installed
A. Repair the Hard Drive and Permissions:
Boot from your Snow Leopard Installer disc. After the installer loads select your language and click on the Continue button. Then select Disk Utility from the Utilities. After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer. Now restart normally.
If DU reports errors it cannot fix, then you will need Disk Warrior (4.3.) if DW cannot fix the drive, then you will need to reformat the drive and reinstall Snow Leopard.
B. Make a Bootable Backup Using Restore Option of Disk Utility:
1. Open Disk Utility from the Utilities folder.
2. Select the destination volume from the left side list.
3. Click on the Restore tab in the DU main window.
4. Check the box labeled Erase destination.
5. Select the destination volume from the left side list and drag it to
the Destination entry field.
6. Select the source volume from the left side list and drag it to the
Source entry field.
7. Double-check you got it right, then click on the Restore button.
Destination means the backup volume. Source means the internal startup volume.
C. Important: Please read before installing:
1. If you have a FireWire hard drive connected, disconnect it before
installing the update unless you will boot from this drive and install the
update on it. Reconnect it and turn it back on after installation is
complete and you've restarted.
2. You may experience unexpected results if you have installed third-
party system software modifications, or if you have modified the
operating system through other means. (This does not apply to
normal application software installation.)
3. The installation process should not be interrupted. If a power outage or
other interruption occurs during installation, use the standalone
installer (see below) from Apple Downloads to update. While the
installation is in progress do not use the computer.
D. To upgrade to Lion/Mountain Lion:
1. Purchase the Lion/Mountain Lion Installer from the Mac App Store.
The download should start quickly. Lion is nearly 4 GBs so a fast
internet connection is essential. Download time could run upwards of 4
hours depending upon network conditions and server demands at the
time.
2. The installer will run automatically after the download is completed.
Click on the Install button to begin the upgrade.
3. Follow instructions for installation.