No, it shouldn't. The city should leave the reserve fund intact and, if anything, should boost it to $220 million to meet its policy target of 5% of the budget. Depleting the reserve fund to cover the shortfall would be worse than fiscally imprudent. It could be fiscal suicide.
Some city leaders apparently think of the reserve fund as a "rainy day" stash, to be used when times get rough. They figure that there is little point to having a rainy day fund if they can't use it when there's a fiscal drizzle, or especially, as in the current case, a deluge.
The first problem with that thinking is that Los Angeles is not simply trying to make ends meet over the next five months in anticipation of some July 1 payday. No such payday is coming. The end of the fiscal year simply introduces next year's trouble -- a budget shortfall perhaps twice the size of the current one. That kind of problem cannot be faced without a prudent reserve, underfunded though it may be, carried over from the current year. The reserve is there to deal with the problems that can't yet be seen (an earthquake, perhaps, or a state budget raid), not the ones in plain view.