When I delegate my XTZ to a baker, what is the reason for the time lag before the delegation seems to activate?
As you can see in the documentation from Nomadic Labs
In Tezos, the right to publish a block in cycle n is assigned to a randomly selected roll in a randomly selected roll snapshot from cycle n-PRESERVED_CYCLES-2.
PRESERVED_CYCLES=5 so this means that effectively baking rights are announced 7 cycles in advance. This means that if you do a new delegation to a baker it will take 7 cycles before this gets reflected into additional baking rights.
Depending on your baker commercial policy he may or may not give you a share of the baking rewards earlier than this but that is entirely commercial since the protocol rules work as indicated above. Please check directly with your baker for practical details about their payment policy.