The way level selection from a pack worked in Lemmini was horrible horrible horrible, you had to click through the menu at the top, there were no keyboard controls whatsoever and when you moved the mouse the wrong way the whole drop-down menu from the top would collapse. x_x
I think it's worth identifying design goals. For instance, it should be convenient to access any level from a 10-level pack or any standalone level.
On the other hand, I remember IchoTolot saying he wants to create an experience with his large level packs, so one might want to have a way to play through them as you'd play through the original game. At the same time, you want to be able to access those levels that you have already beaten in a convenient way, and view the whole level list.
With these goals in mind, here's a possible solution. The menus could retain the authentic look from the original game, while the listings/file browsers could look like any modern file list would look like:
Lemmix main menu:
Browse levels
Play level (somewhere the current level name/preview should be displayed)
Load level pack (multi ranking pack)
Options
Browse levels: file tree that can be navigated to find standalone levels and .DAT packs. Here .DAT packs could be treated like folders, maybe. Accessible from /anywhere/ via Ctrl+O or some shortcut like that.
Play level: Ideally, at least IMO, it would skip the preview screen and all the relevant info should be displayed ingame. After beating a level, the next level in the file tree could be selected, or the level browser could pop up again.
Options: ideally also accessible via shortcut from anywhere, and maybe also part of the level pack menu. Maybe some designers also want level pack specific options?
Load level pack: Browser for complete packs. When loading a pack with multiple ratings etc, a new menu would show up basically akin to the original Lemming menu, with ratings and a title bar displaying the pack name (either designed by the pack author, or a simple text placeholder).
Level pack menu:
Rating (as in the original game, change with up/down or similar).
Play level (first unsolved level in currently selected rating)
Browse level list
Exit to main lemmix menu
Browse level list: List all levels in each rating, allow to play any you've beaten or enter an unlock-all code (now here's something Lemmini did well in a way). Either way the cumbersome password system should be avoided. This is just for convenient access to arbitrary levels which is desirable.
Play level: upon solving a level the game should just move on to the next. Preview screen could remain for authenticity.
I'm just treating level packs specially here as I feel some people might want them to feel like the original game. Otherwise they could just be treated like a file tree (and I still think they should also be implemented like that instead of a binary blob, but that's a different issue).