The month to month contract between tenant and landlord state 30-days to be given. Tenant gave 3 days notice, can the landlord charge the tenant for lost rent?

Not only can the landlord charge them for the entire month. They can be taken to court to get a judgement for that money. And get a Writ of Garnishment to collect it through a number of means.

Yes, if the tenant does not give proper notice, then they can be charged for rent until the end of the notice period or until the unit is relet whichever is sooner. The tenant's security deposit can be applied towards unpaid rent.