Is it possible to get a pinched nerve as a result of lifting weights?

Yes. Disc herniation can occur secondary to overloading its weight bearing capabilities as a disc is designed for carrying & distributing load as well as allowing for motion. Sometimes it is not just the amount of weight lifted but the incorrect way it was done or even related to a repetition mode of failure. Conditioning or lack of may also play a role as can muscle fatigue placing more load on disc.
Yes. Thats why they tell you to exhale when lifting. Holding breath while liftiing increases intrabdominal pressureand vetebral disc pteesures herniation can occur and pinch a nerve cause leg pain siatica.