Not the most elegant solution, but what I do in these situations is the following:
This leads to some manual overhead in maintaining my LyX file in sync with the co-author's plain tex file, but in practice it turned out not to be a big problem. Often when I find that the re-imported document is fine in terms of layout and edits, I simply replace the old one with the new one. Also, if I find that something in the layout is inconsistent and the document import does not deal with it properly (e.g., optional short titles in definitions), this can be fixed in the layout by layout modification so as to require a proper number of arguments.
Regarding loosing formatting, this was never a big deal to my co-authors, except for demands not to break lines, but instead rely on text-wrap at the end of lines. This can be helped with Menu/Tools/Preferences/Output/General/Output LIne Length.
Well, usefulness of an advice like this of course depends on the particular modus operandi of you vs. your co-authors so YMMV.