Can I use the HEK293T cells I used to make lentivirus to create a stable line with the construct I was packaging by treating the cells with puromycin?

No, you will not want to use the cells that you have already transfected (to create the virus) because the packaging plasmids would still in the cells and they may or may not interfere with your assay. Also, the VSV-G envelope for pseudotyping the virus is toxic to the HEK293T cells and they will eventually die.