What's the point of lzcnt when there is already bsr?

They behave differently, when the value consists of all zeros.
BSR searches for the highest bit that is set to 1, and when there's no such bit found, it returns with ZF cleared, and destination not modified.
On the other hand, LZCNT counts the amount of zeros from the highest bit, and when the value consists of all zeros, it simply returns the amount equal to the size (in bits) of the source operand.

Minor correction: Although what you say may be true in practice, the docs state that the dest is undefined in that situation. So it is probably best not to rely upon any unmodified behaviour.

And don't forget that LZCNT is AMD-specific and AFAIK Intel is not going to implement it. Let me know if I'm wrong.

Why, though? Patents? Pride? I can't see the harm in both implementing such instructions, but I don't know what goes on behind the scenes.

I'm not sure. Competition and different roadmaps perhaps. And important players' opinion matters I think. If developers of Visual C++ tell Intel "hey, there's LZCNT which could be useful", they can force them to implement it.

BTW, there are Intel forums where you could ask. The Intel guys are pretty responsive.