It seems Harry Beck didn't confine himself to designing non-geographic Tube
maps. I came across this Imperial Airlines air route map he created in
1935:

https://pbs.twimg.com/media/DNOBfs-W0AA3KJm.jpg:large

Air routes were rather infrequent back then, and Beck came up with a rather
complicated way of showing weekly, twice-weekly, etc frequencies. It seems
that even back then, airlines had alliances, but were more open about
code-shared flights than they are today.