My son has no lining in his stomach and he has ulcers. Could having those problems cause blood to be in his stool or is that something really wrong?

Yes. See a gastroenterogist because this is a serious problem and needs good medical attention. .
Yes, If blood in the stool is bright red, it could be coming from the ulcers, but that suggests he is bleeding a lot and needs early intervention. Slow bleeding in the stomach or upper intestine usually becomes black or hidden as it reaches the rectum. Red blood usually arises from the lower intestine but all blood in stool needs evaluation unless there are known hemorrhoids and blood is only on TP.