Rosetta, which was licensed by Apple to run PowerPC applications (after the switch to Intel CPU's) is no longer available to be run in Lion.
Your best solution is to upgrade Final Cut Studio 2 to a version that is native for Intel and will run in Lion.
To install software from a CD/DVD, you need to purchase the external USB DVD drive from Apple, or use CD/DVD Sharing of the drive from a networked computer.
If you are unable or unwilling to upgrade your copy of Final Cut, you could install Snow Leopard (and Rosetta) into Parallels 7 in Lion (these steps will require a DVD drive to access your copy of Snow Leopard Install DVD:
In half a word, it looks like he has the latest MacBook Air, which comes with Lion and hence cannot have Snow Leopard (re)installed...
There is quite a bit of controversy in the editing community, that the latest version of Final Cut Pro (which happens to be the Lion compatible version) has been "dumbed down." Further, the latest version does not accept the earlier version's raw editing files; they must be converted.
Hence to keep the earlier, more robust version of Final Cut Pro working on a Lion-only computer, his only solution would be the Snow Leopard (and Rosetta) installed into Parallels 7 in Lion solution that I suggested above. Obviously a virtualization solution is not optimum for a program such as Final Cut Pro, but short of purchasing a 2nd older computer (he did not even purchase the external USB DVD drive), what other options does he have?
It may be a full price purchase and not just an "upgrade price" to previous users. In the Mac App Store, v10.0.4 lists for $299.99. You do this throught the Mac App Store application and hence you will not need a DVD drive for your MacBook Air.
However, note the consumer comment online about deficiencies on the latest version:
including this one (you may want to do some research with editors who have worked with this and the older versions, depending upon what your needs are for FCP):
"This is no longer a pro tool!
by Michael Hilliard
"This is my third version of FCP over the past five years and I really thought I'd justify the purchase based on past usage. But it turns out the application isn't really a PRO tool any more, just an oversimplified home video editor. I make video segments using a combination of action and stills and FCP has been terrific for that in the past, but FCP no longer supports custom resolutions - one of the most important features for my clients.
"I was really looking forward to the new methods for editing - they seemed like a good progression from FCP6, and I have to say the live previews are pretty nifty. But I didn't realize Apple was going to burn the professionals in the FCP community in favor of downgrading this to a consumer tool. I just wasted $350 and I'm very, very unhappy."
So you purchased Final Cut X since your OP? And from your last sentence "because..." it appears that you are another unhappy user of Final Cut X; sorry to hear that. I have no experience using Adobe Premiere, so I cannot advise you there.
Would using your original FC2 in Parallels be a better situation for you?
I did some research for you on this issue...
Going back to last year, there is a thread here that claims you are able to install FCP 6 (FCS2) on Lion after installing Rosetta from your Snow Leopard Install DVD.
The theory seems to be that once Rosetta is installed into Lion, it will allow Lion to run PowerPC install procedures only, so long as the ultimate program can run in Lion without Rosetta. I did not think much of this theory until I saw that babowa confirmed the procedure and she is a well respected poster here.
Here is the link:
You still have the problem of not having a DVD drive, but the Air can access the DVD drive of another computer over a network through the Sharing Panel in System Preferences on the other computer (or you can borrow someones external USB DVD drive, or buy one from Apple for about $99).
If you run into any other problems, come back for more help. If it works, please report back your successes!