Usually, the word 'bloodlines' is used for animals.
Dictionary definition of lineage
.
1.
a. Direct descent from a particular ancestor; ancestry.
b. Derivation.
2. The descendants of a common ancestor considered to be the founder of the line.
For example, I am an Australian Lithuanian.( My parents were born in Lithuania, but I was born in Australia)
His/her father is Japanese and the mother is American ( double nationality maybe)= He/she is an American Japanese. OR He/she is of American and Japanese parentage.
His/her lineage is that his/her grandfather/great grandfather was Italian but he/she was born in Australia= He/she is an Australian of Italian descent.