Sorry to learn about your mom's condition.
As far as life expectancy is concerned, stage 4 lung cancer
life expectancy can vary considerably among different people.
Stage 4 lung cancer encompasses several lung cancer types, and includes cancers that have spread to only one distant region or those that have spread extensively. Since the metastasis had occurs to various distant regions,the outlook looks still more bleak,as there are many other associated co morbities also.
If docs are providing treatment ,then they at least have hope of extending life, quality life, for the person we are talking about it here. I would advise that since that time cannot be precisely measured even in the worst case scenario, that it be lived as if every day were the last, spent enjoying life, friends, family, spent loving and laughing.
Keep giving her good treatment and good psychological support and care and forget about the timing of death,which nobody can tell.