The installer for Logic 8 uses ppc code which was native in 10.5.x and achieved through Rosetta in 10.6.x. This has now been dropped completely in 10.7.x.
If you still have your old laptop or another Mac that will let you run the installer you can put your new Mac into firewire disc mode (hold t key whilst booting), connect the two machines together with a firewire cable and choose the mounted disc of your new Mac to install to.
Secondly, I believe you can actually drag and drop the content of Logic 8 although there are quite a few folders spread throughout the system.
When the installer fails, does it give any filename of where it failed? For example, trying to run the updater for illustrator CS3 on a Lion Mac fails saying the file nspatch is PPC code. By swapping that one component out with an Intel compiled nspatch it makes that particular installer work.
Anyway, once you have Logic 8 on your new system there is a trick to make it run given to us by Robert Davies from this very forum soon after the release of Lion. It is:
Find your Logic Pro app and ctrl click (or right click on it)
Then click 'show package contents'
Then in the resulting folder, double click on 'contents'
Then double click on 'Mac OS'
Finally double click on the file named 'Logic Pro'.
I hope some of this helps.
No. You're using your old computer as a buffer. Make sure your new laptop is in Firewire disk mode and connected to your old Mac. The HD of your new Mac should show up on the desktop of your old Mac. When you run the Logic 8 installer it should ask you for a destination drive. Choose your new Mac HD that is mounted on your Desktop.