For what length of time do stage 4 lung cancer patients usually survive?

Limited. Personal, risk factors and cancer stage. If stage 4 with distant metastasis, then with best care 2-5 years is possible.
Stage 4 lung ca. Unfortunately many patients with lung cancer are diagnosed with "late stage" disease - either 3 or 4 - meaning it has spread outside the lungs. Fewer than 2% of stage 4 patients live 5 yrs. In fact, most with stage 4 will survive less than a year. At this stage, some patients elect to have chemo +/- radiation, but a lot of patients also elect palliative (comfort only) therapies.