How do lines of longitude change as they get further from the prime meridian?
They really don't.
All "lines" of longitude are actually half-circles that run from North pole to South pole. They all have the same length. But of course they are more East or West of the prime meridian (=the one going through Greenwich UK).
"Lines" of latitude do change. They are (whole) circles parallel to the equator, and as you go north (or south) the circles become smaller, untill at latitude