Can a child be baptised into the Catholic church but dedicated into the Lutheran church too?

My non-expert opinion: The RC baptism would be considered valid, I'm reasonably sure, regardless of what the parents do re: the Lutheran church. But baptism only gets you so far. There will be the matter of confirmation, and eventual church membership. The RC church would almost certainly disallow 'dual-citizenship'. The Lutheran church is like RC in a lot of ways, but is not within the RC communion.

Roman Catholic AnswerA child could only be baptised in the Catholic Church after the parents have attended classes, and then, at the baptism itself, made solemn promises to bring the child up as a Catholic. Anything like a "dedication in the Lutheran church" would be considered apostasy - a very serious sin. I do not think such a situation would occur except in, perhaps, a mixed marriage, where the couple was thinking of having the Lutheran service to pacify the in-laws. This, again, would be a serious breach of their duty towards their child and they should discuss this with their priest.