Lyx 1.3.3 and 1.3.4 (and maybe previous versions) have odd behavior when editing the last line before an offset equation. If you position the cursor to add something to the end of this line, as soon as you start to type the cursor jumps to the beginning of the line. The text still appears in the right place, so after figuring this out, it is still possible to do what you want to do. However, the behavior is rather confusing. The same thing happens just before an open footnote.
Dave Raymond