To type in such a way that you spell out how a word sounds, rather than how it's actually spelled. This is often confused with being bat fucking retarded, but in actuality is used to mock people with no ability to find and use a spellchecker.
Occasionally, one might use lawllyspeek so often that they become bat fucking retarded.
John: "Hayyyyyyy maahn. Ai herd yu wer saein' shit uhbowt mi last niteeeee. Wehl fuk yu."
Jack: "Seriously? Shut the fuck up and die, thanks."
(translation from lawllyspeek for the illiterate: "Hey man, I herd you were saying shit about me last night. Well fuck you.")