To logically arrange the sentences concerning the sequence of a bedtime routine, consider the natural progression of activities. The first activity is generally personal hygiene, followed by relaxation and sleeping preparation. Here is the logical sequence:
1. B: He brushed his teeth.
2. D: He read a few pages of his book.
3. C: He lay down on the bed.
4. A: He switched off the lights.
The sequence "B, D, C, A" reflects a plausible and natural order of actions one might follow in a bedtime routine.