it was unclear if Lampreys and Hagfish were related or whether the Hagfish was a degenerate form of Lamprey which seemed to be the case from morphological arguments. However new fossil evidence and DNA has now shown they are independent and both were around at the same time long long ago.
Title:agfish from the Cretaceous Tethys Sea and a
reconciliation of the morphological–molecular
conflict in early vertebrate phylogeny", Miyashita et. al., 2018.
Summary: "Hagfish depart so much from other fishes anatomically that they
were sometimes considered not fully vertebrate. They may
represent: (i) an anatomically primitive outgroup of vertebrates
(the morphology-based craniate hypothesis); or (ii) an anatomically
degenerate vertebrate lineage sister to lampreys (the
molecular-based cyclostome hypothesis). This systematic conundrum
has become a prominent case of conflict between morphology-
and molecular-based phylogenies. To date, the fossil record
has offered few insights to this long-branch problem or the evolutionary
history of hagfish in general, because unequivocal fossil
members of the group are unknown. Here, we report an unequivocal
fossil hagfish from the early Late Cretaceous of Lebanon. The
soft tissue anatomy includes key attributes of living hagfish: cartilages
of barbels, postcranial position of branchial apparatus,
and chemical traces of slime glands. This indicates that the suite of
characters unique to living hagfish appeared well before Cretaceous
times. This new hagfish prompted a reevaluation of morphological
characters for interrelationships among jawless vertebrates.
By addressing nonindependence of characters, our phylogenetic
analyses recovered hagfish and lampreys in a clade of cyclostomes
(congruent with the cyclostome hypothesis) using only
morphological data. This new phylogeny places the fossil taxon within
the hagfish crown group, and resolved other putative fossil cyclostomes
to the stem of either hagfish or lamprey crown groups.
These results potentially resolve the morphological–molecular conflict
at the base of the Vertebrata. Thus, assessment of character
nonindependence may help reconcile morphological and molecular
inferences for other major discords in animal phylogeny"