【Lineal】 , 【linear】  share the basic meaning of or relating to a line or lines, but they are clearly distinguished in their specific senses.

【Lineal】  is more often applied to a direct line of succession from or to a common ancestor either physical or spiritual, and is often distinguished from collateral, thus, the  【lineal】 descendants of a man would include all his sons and daughters, all his grandsons and granddaughters, all his great-grandsons and great-granddaughters, etc..

【Linear】 tends to lay the stress on a relation to a line other than a line of succession, either in fact or in likeness; often it suggests a relation to something having or felt as having one dimension only, usually length, especially in contrast to what has two or more dimensions.