This information is largely adapted from this guide intended for Touhou.

Disclaimer: While I haven't noticed any issues with them, follow the download links at your own risk.

Note that a copy of Lemmings is not provided here. You will have to find that yourself.
The emulator: The Touhou guide recommends using the unofficial fmgen build, available here (scroll down until you find a file called "np2fmgen.7z" - 7zip is required to extract it): . Lemmings doesn't appear to use any features that benefit from this build over the official one, but relevant to Lemmings, there is a speedup function in the fmgen build. The audio emulation is noticeably better for some games in the fmgen build, but Lemmings seems to emulate plausibly well in both versions (I don't have real hardware to compare to at this time). The rest of the guide will assume the fmgen build, though much of it will work in the official build.

Configuring the emulator: There's multiple executable files in the fmgen build download. Multiple of them will probably work, but I'd suggest using np21nt.exe. The colors will look super wrong by default. You can improve this considerably by turning on Real Palettes (under the Screen menu). It doesn't seem to be perfect, though - I don't know if it's an emulation problem or if that's just how the PC-98 port is. Also, go to Emulate -> Configure, and set the multiplier next to the CPU selection. 32 should work okay, but if the performance seems bad, experiment with it a bit. I got bad performance when this was too low as well as when it was too high. Unlike DOSBox CPU cycles, however, I didn't seem to notice any immediate changes when messing with this - you'll probably need to reset to apply the changes.

Launching the game: You'll need to mount the disk image. If you've got a harddisk image, mount it as one of those (Harddisk -> IDE #0 or SASI #0 depending on build); if you've got a floppy disk image, you'll want to go to FDD1 -> Open (no guarantees they both exist). Then, go to Emulate -> Reset and it should start up. F12 should activate the mouse. If it doesn't, go to Device -> Mouse.

Even though the emulator download link is dead (and I'm genuinely not sure where I found it recently, sorry about that), I would like to add a few things on top of this based on my own experimentation:

The PC-98 version actually has its own fast-forward feature, so if you find the vanilla version of the emulator, you aren't at a disadvantage The reason this fast forward feature is so obscure (aside from the manual being both Japanese and unscanned) is probably that the fast forward key (that WOULD be one key to the right of P - the pause key - on an actual PC-98 keyboard) gets mapped to END in Neko Project II (which, depending on your keyboard, you may have to hold down Fn to even use!), and there is unfortunately no way to change that without using other software.

If you wish to use the in-game fast forward feature, x32 for the CPU multiplier isn't the best choice. Much like the Windows version, fast forward speed is, to an extent anyway, dependent on CPU speed. x8 seems to offer the best balance, and it is the most accurate to models sold around 1991. Levels with large amounts of water or large OWWs may result in some slowdown, but the PC-98 version features the same performance compromises as the MS-DOS version (removal of decorative water and limiting all levels to 80 lemmings) so slowdown is relatively uncommon, certainly less common than in any 100 lemming version. Cranking it higher will mitigate slowdown and increase fast-forward speed, especially when many lemmings are in the level/onscreen. Setting the multiplier lower than x6 (which would correspond to lower-end models and older models at the time) is not recommended.

As for the colors, there is a setting called "Real palettes adjust"--frustratingly buried in a dialog box--that can fix the colors. Go to Screen -> Screen option... and the dialog box will appear. Select the Timing tab and slide "Real palettes adjust" to -31, and the colors will be completely correct.

One last thing: by default, the few voice samples in the game are downright ear-piercing and extremely unpleasant to hear. This is only because the emulator is not set up for accurate playback of samples through the PC Speaker or the PSG by default. This time, the setting is buried in the .INI file... which, by the way, only exists after opening the executable at least once. Search for the setting BEEP_PCM, which is set to 0 by default. Set it to 3, and the emulator will now use a different strategy for playing samples through the beeper and PSG, and the samples sound MUCH less bad as a result.