No, lush means to be bursting with life, or to be rich and pleasing. I usually think of it in terms of the beautiful green lushness of the rainforest, if that helps. However, the urban dictionary defines it as a slang term for cool or good, so if you heard it in that sense, I guess I could understand how you thought it meant encouraging. I hope this answers your question! :D
While many might say the fridge needs to be opened first to prepare breakfast, note that it does not say that the parents are in the house, and therefore they would need to be let in. Hence the answer of what to open first would be "the door".
