LaTeX: /ˈlɑːtɛx/ LAH-tekh, also pronounced as /ˈlɑːtɛk/ LAH-tek or /ˈleɪtɛk/ LAY-tek
Knuth, in his book, memorably decreed a pronunciation (and case mixing in the written form) for TeX, with a hard /ch/ at the end (literally, "your monitor should become slightly moist"), backed by a clever and erudite rationale involving the etymology of words like technique.
Leslie Lamport, in his book on LaTeX, decreed a case mixing, but (as you say) ok'd any reasonable pronunciation.
Originally, a TeX user would've been called a TeXnician, which, according to Don Knuth, would be pronounced the same as "technician."
Yes- it comes from the same root.
I guess we're in the same boat on that one. It's a weird pronunciation, though, so it barely counts against us. ;)