Exactly so - the issue was that you were sort of stuck based on when you had to reload. The thinking was that it was better to finish the drum off rather than fly on and go into a subsequent fight with an unknown amount of ammunition (and possibly go empty at the wrong time). Better to go into the next fight with a fresh drum. The reloading issue is most pronounced on the early airplanes - fewer rounds in the drum and the mount requires you to stand, or at least sit way up to reach up and change the drum. The sliding Foster mount later helped in that regard, but there remained the problem of wrangling with a full drum and then sliding the loaded gun into place. A loaded 97 round Lewis drum is quite heavy for a pilot who is also flying the plane, let alone adding that to the machine gun and then having to slide it all back into place.
Yet despite all of that, the British persisted with the over-wing Lewis system through 1917 (various Nieuports) right into 1918 (SE5a for example). Albert Ball in particular was fond of the system, where he would attack two-seaters from underneath, with the Lewis gun aimed upward. The SE5a became known as a mount of "aces" because of its superb flying characteristics for that time, and many British aces were comfortable and successful using the mixed Vickers and Lewis system. Many aces also cut their teeth on Lewis-only Nieuports.
And the over-wing Lewis system did have a couple of advantages. First, the rate of fire without a synchronizer was relatively high. Second, the gun did not rely on a synchronizer to be operated safely. The synchronizer gears, especially the early ones, had to be "tuned" and sometimes failed. The Lewis gun is also a relatively lightweight machine gun, so the firepower-to-weight ratio was not bad on the Lewis. Even if the Lewis with drum was a lot of weight to be sliding around while trying to fly the plane, it still was lighter than the Vickers or Spandau/Maxim.
Ultimately the route forward was two synchronized machine guns in front of the pilot. The design of the Spad XIII and the Albatross/Fokker fighters proved to be better once synchronization became reliable and rate-of-fire improved on the fuselage machine guns.