To add to what's already been said, there are some old 122 (and most other LT routes) timetables / allocation details on the 'l
ondon bus route histories' website, which may be of interest if you haven't met it.
As others have said, running in overlapping sections was one way of providing more of a service in the busier middle bit of a route - e.g. some buses would do Slade Green - Forest Hill, others would do Bexleyheath - Crystal Palace during Saturday daytimes (it might vary at different times of day / week, and in LT days, many buses at start and end of day would run to/from garage to somewhere in the middle of the route or vice versa (as in early morning / late evening journeys terminating at Lewisham.)
A few routes (from memory, the 12 and 279) ran in 3 overlapping sections at least some of the time, and in the 1970s the 141 was possibly unique on Saturdays in that the two sections didn't touch (Wood Green did Wood Green - Moorgate and new Cross did Grove Park - Elephant with a few early morning journeys to Farringdon Street for print workers coming off night shift.)
Some routes had overlapping sections like I've described on the 122, sometimes it was more complicated, e.g. if a route ran from A to D via B and C, each bus might do a cycle of A to D, D to B, B to C, C to A rather than the more obvious option of having one section doing A to C and the other B to D in each direction.
The reason behind some of this was to make chunks of duty either side of a meal break and / or in the day so that they would fit the legal / LT agreement for duties. An obvious example, but if you have a route where the garage is at one end of the route, and a round trip is about 3 hours, that doesn't really work, as 2 round trips is a bit short for a day's work but too long for a single spell of duty, 3 round trips is probably too much for a day, so you need either remote meal breaks, or a scheduling way of making each chunk of duty a better length.
This was also a factor in many of the routes that different things on Sundays - although some served specific traffic objectives, like the 124A to Bexley Hospital for visitors, some south London services extending to Aldgate for the Sunday markets.
Bits of different routes could be stuck together to make either the vehicle or duty schedule more efficient. The 122A was an example of this in the late 60s, the Woolwich - Erith bit only warranted a 30 minute headway, but the round trip was only just over an hour, so doing it with 3 buses would have been inefficient - hence it was extended via the 122 route to Crystal Palace (until the 122A went OMO anyway.)