There should be grease on the locking lugs to begin with but you just need to clean everything well and get that rust out. Use a lug area cleaning kit and an AR style chamber brush so you can scrub the front of  the locking lugs when are rusted and clean it all out. A cheap kit like this and the addition of the AR style chamber brush works fine. Tipton action chamber cleaning kit

After cleaning and drying grease the lugs on the bolt and also back near the bolt handle where it rotates into the action when closing bolt and work the bolt a few times. Holding the trigger down when doing this will help distribute the grease better as it takes some tension off the bolt.

When you say chamber do you mean the actual chamber area where the round goes? If so hopefully no pitting but just clean the chamber and bore well and put some oil on it before storing it.