My lease ends May 25th. Notice given April 22nd. They're stating I must give 60 days notice or pay penalty of 2 months rent.

You have an interesting situation given the Covid-19 pandemic. You don't say whether there is a security deposit and whether it covers the two month's rent. I assume that you are going to move anyway, regardless, so I will answer the question with that in mind. You should notify your landlord that there is a doctrine of "force majeure" which essentially excuses a brach of contract whenever there is an unforeseeable circumstances that prevents someone from fulfilling the contract, like a hurricane, or war, or Covid-19. The rub is that there is a real question whether the cuircumstance prevented you from giving notice. The landlord may say that you could and should have given notice. The lockdown order would have prevented you from vacating as intended, but it may not be an excuse or defense for failing to timely notify the landlord. Regardless if you assert the defense, you may create enough uncertainty that the landlord will not take further action (in fact, few landlords pursue tenants for small amounts of money because even if a judgment is obtained, it is usually either uncollectible, or too expensive to collect). In any event, good luck, stay safe, and be well.