Are you trying to change the document class of (a copy of) the tutorial file? If so, the messages you are getting are to be expected. Not every document class supports every environment known to (some) other document classes. For instance, I just opened an old slide show (Beamer document class) and arbitrarily tried to convert it to Article (AMS). The slide show has a paragraph that uses the "Institute" environment (to indicate the speaker's affiliation). Beamer knows what that is; Article (AMS) does not. Each frame (slide) begins with a "BeginFrame" environment, and Article (AMS) has no idea what that is.
Clicking one of the messages should take you to the text that has LyX confused. LyX will not delete anything from an unrecognized environment (layout); it will just mark the environment as unrecognized (for instance, "Institute (unknown)" in the environment drop-down. It's up to you to select an alternative environment understood by the new document class. Paul
