Sometimes the mystery and the not-knowing are more satisfying and enjoyable than solution.
There is a Lethbridge Road just off Woodwater Lane. It’s not on the 1938 Land Utilisation Survey, but is on the 1945 OS map, as is Peryam Crescent, which replaced the junction of Woodwater Lane and Salter’s Road.
Lethbridge Road also crosses the Northbrook, and I entertained thoughts that the name derived from Lethe Bridge, Lethe being one of the five rivers of Hades, the river of forgetfulness. A romantic classical connection. However, there are Peryams and a Lethbridge among the list of Exeter mayors during Tudor and Stuart times, so there is probably no need to look further back than that.