Can lack of vegetables and calcium have a serious effect on the digestive system

Not really, those 2 usually provide nutrients to keep other parts of the body health. i.e. calcium for strong bones etc

however vegetables can help improve your digestive system by providing lining on the walls of your intestines.

Still, I'd advise you to eat plenty of both, if you lack calcium you can develop osteoporosis in your latter life, and if you lack veges you'll become constipated and have a range of other health issues, since veges provide you body with so much nutrients that meat alone cannot provide