The error you mention happens when the level file refers to a terrain piece that you don't have installed in your styles folder. When you say yes, NeoLemmix will try to download the style containing the piece.
If you get the same error again, this means one of two things: either the level is missing pieces from several styles, and after you have downloaded them all, it will work; or the download file NeoLemmix has access to is also missing the piece.
To determine which of these it is, try downloading the full styles download from here:
https://www.neolemmix.com/download.php?program=52(On a side note, Lunatic is the
last rank of Lemmings Redux. The intended playing order is Gentle, Quirky, Zany, Manic, Lunatic.)