If there's 8GB's of RAM that should be more than sufficient for Logic Pro.
Doubtful changing the hard drive would make any difference but for the lag issue, you should Verify the hard drive.
Launch Disk Utility located in HD > Applications > Utilities
Select the startup disk on the left then select the First Aid tab.
Click: Verify Disk (not Verify Disk Permissions)
If Disk Utility reports errors, to make repairs startup your Mac holding down the Command + R keys.
From there you should be able to access the built in utilities to repair the disk using OS X Recovery.
If Disk Utility says the disk appears to be ok, a Safe Mode boot deletes system caches that may help the lag issue.
Top left corner of your screen click the Apple > Shut Down.
After your Mac shuts down, wait 10 seconds, then press the power button.
Immediately after you hear the startup tone, hold down the Shift key. You should press the Shift key as soon as possible after you hear the startup tone, but not before.
Release the Shift key when you see the gray Apple logo and progress indicator.
Once you are in Safe Mode, go back to the Apple menu. From the drop down menu click: Restart
About Safe Mode
