For squamous carcinoma cancer of the lung, how long can you live without any treatments or surgery?

Variable. There is wide variability by lung cancer type, stage of the disease and individual characteristics so that it is not feasible to provide a meaningful estimate of survival. See this site for more information.
12-18 months on avg. Depends on the stage but, in general, 12-18 months without treatment. Some very small cancers may grow slowly, if at all, but that's unusual and hard to predict. Why no treatment? Is the stage too advanced? Are there severe other medical conditions? There are both surgical and non surgical options.