Within such a list environment, things are within its text area and not in the outer page area. In a logical structure, the list environment should end before another displayed item comes centered between the page margins. Resuming one list is easy, resuming from nested lists can get messy, which ...
there was no quick answer, perhaps because the code was not included here. Very good that you made an example, but please post it as code here in the forum, instead of an Internet link to some external service.
If you embed an equation within an enumerate list, it gets centered in this list ...
when I uncomment these two lines, it runs for me without error, also a second and third time with the .aux file present.
Perhaps post the corresponding section of the .log file here, as the error message is not mentioned here.
I recommend using Latin Modern for a high-quality font that looks like the default font, with \usepackage{lmodern} in the preamble (or an equivalent LyX setting). The default font looks bad with modern font encoding for French. Another way to improve this would be ...