Diablo 2 & Wine Compatibility
I downloaded the Diablo II installer from the Blizzard site and was able to install it under Wine 1.3.15 on Ubuntu 11.04 without issues. If you run into issues while using CDs, don't forget that you can add your game serial number to a Battle.net account and download it.
One annoying issue was holding ctrl would move the window instead of showing all dropped items. I believe you can change this from the winecfg options.
The WineHQ application compatibility database has some information here:
http://appdb.winehq.org/objectManager.php?sClass=application&iId=74
The retail version seems to work well.
http://appdb.winehq.org/objectManager.php?sClass=version&iId=49
What works
Everything (Gameplay, videos, loggin in, battle.net)
Sound works better after updating from 1.12 to 1.13
What does not
Nothing that I can think of
What was not tested
Nothing that I can think of
Sounds like your install issue is related to the game disc itself.
According to WineHQ, D2: LOD runs on Ubuntu 11.04 with a platinum rating (Which indicates "Applications which install and run flawlessly on an out-of-the-box Wine installation"). Vanilla D2 gets a similar rating running on Ubuntu 10.04.
It sounds like you have your original CD Key so I would recommend using Battle.net to turn your CD Key into a digital download, then redownload the game via the Blizzard downloader (which also runs under Wine, of course).