Honestly the landing strip theory never fully convinced me. The lines are flat but the surrounding terrain is rugged as anything, you'd need more than some scraped desert floor to land something safely.
What does interest me more is the alignment angle. A lot of the longer lines track solstice and equinox positions pretty accurately. Could be agricultural calendar stuff, could be ritual procession routes, could be something else entirely. I lean toward the ley line / energy corridor idea myself, similar patterns crop up in pre-Columbian sites across the whole continent.
The sheer scale is what gets me though. You can only really appreciate the shapes from height, which raises the obvious question of who were they made for. Doesn't have to mean aliens but it does mean something.
Anyone looked into the connection between Nazca and the Paracas culture? There's some overlap there that doesn't get discussed enough.