Legal Question in Real Estate Law in California

It would help if your lease explicitly gave you sign rights. In that case, the landlord has breached the lease. If not, you would have to convince a court that the signage rights were implied in the lease.

That's not a very complete answer your landlord gave. He's probably trying to tell you that your lease doesn't allow that kind of sign. It could be there is a provision against violating any law, and the sign violates a zoning ordinance; or the lease precludes structural modifications without prior approval, and the sign came under that provision. You should ask for a clarification.