I would use 'lodged up' in two cases: If somebody is staying someplace up above you or north of you, we could say 'lodged up'. "He's lodging up on the third floor." "He is lodged up in Akron." However, you seldom hear that phrase anymore. Second, you would use it when something has been moving and comes to rest someplace, usually in some tight space. "The bullet is lodged up in his brain." "He had dust particles lodged [up] in his eye by the wind."