LyX is not available for iPad but there are a few alternatives with similar functionality. The best iPad alternative is Scrivener. It's not free, so if you're looking for a free alternative, you could try VerbTeX LaTeX Editor or iText. If that doesn't suit you, our users have ranked more than 25 alternatives to LyX and three of them are available for iPad so hopefully you can find a suitable replacement.
VerbTeX is a free, collaborative LaTeX Editor. It allows you to create and manage LaTeX projects directly on your Android device and generate a PDF by using Verbosus (Online LaTeX and Octave Editor) "The Best Way to Type LaTeX on the Go" - androidappsreview.
iText is an intuitive and refined text editor with word processing completely rewritten in Cocoa (so works with Afloat), and is suitable for both Power PC and Intel Macs. iText provides the simplest way to make gorgeous manuscripts on your Mac!