The last element of the lanthanide series is: 

The "f-block" of the periodic table is where the lanthanides and actinides are mostly found. Scandium (atomic number 21) and yttrium (atomic number 39) are occasionally included in the group of 15 elements known as the lanthanides, which has atomic numbers ranging from 58 (cerium Ce) to 71 (lutetium Lu). As a result, we may conclude that lutetium is the last member of the lanthanide series.

The series in which elements are present in between cerium of atomic number 58 and lutetium of  atomic number 71 is commonly known as the lanthanide series.

 We can conclude that lutetium is the last element of the lanthanide series.

Hence option B is correct.