Why are lancelets grouped in the same phylum as vertebrates?

Because they both belong to the Phylum Chordata in which they are both chordates (chordates are defined as organisms that possess a structure called a notochord, at least during some part of their development).

Phylum Chordata

Class Cephalochordata (lancelets)

Family Asymmetronidae Family BranchiOStomidae

Subphylum Vertebrata (vertebrates)

Class Cepalaspidomorphi

Superclass Gnathostomata (jawed vertebrates)

Class Chondrichthyes (rays, sharks)

Euteleostomi (bony vertebrates)

Class Actinopterygii (ray-finned fishes)

Class Sarcopterygii (lobe-finned fishes & terrestrial vertebrates)