Can The Governor Cut The Lieutenant Governor's Budget by Two-Thirds?

Accoprding to news accounts (here), the Governor in signing the budget has cut the budget of the Lieutenant Governor's office by approximately 65%. Can he do this? Cases such as Scott v. Common Council, 44 Cal. App. 4th 684 (1996), suggest that budgetary authority can't be used to interfere with the ability of a constitutional officer to perform his or her duties. And 65% seems like a pretty major cut.