What can you expect in the final stages of metastasis lung and brain cancer?

Prognosis. Obviosly prognosis is not good in this situation. Usual treatment is palliative to keep patient comfortable. Radiation therapy can help neurological symptoms. Disease widening with increase shortness of breath, respiratory failure, pneumonia, infection and pain related to cancer can happen. Palliative chemotherapy can help to improve symptoms.
It depends on the. Size, number, and location of the mets. Mets cause swelling, which can result in headache, nausea, weakness, seizures, or difficulty with thinking, speech, or vision depending on the part of the brain. In patients who succumb to the mets, it is usually swelling leading to difficulty breathing and loss of consciousness. Steroids and radiation (possibly surgery) are treatments that may help!
Variable. Symptoms are obviously variable, but the best i can describe them, they are most similar to alzheimers, but much, much faster. If the worst thing about alzheimers is how long it goes on, the "best" thing about end stage brain tumors is how short the suffering tends to be. Lung cancer can add some shortness of breath and difficulty swallowing as well as lack of appetite.
Depends on location. The extent of the spread will affect the symptoms. It sounds like you are referring to lung cancer primarily with spread to the brain. If the brain cancer is not controlled, progressive symptoms from the mass effect in the brain include headaches, seizures, nausea/vomiting, weakness, blurred vision. In the final stages, the oncologists are very good working with palliative care.