Billions of COVID-19 vaccines have been administered, but many remain hesitant. Misinformation about the COVID-19 vaccines and other vaccines, propagating on social media, is believed to drive hesitancy towards vaccination. The ability to automatically recognize misinformation targeting vaccines on Twitter depends on the availability of data resources. In this paper we present VaccineLies, a large collection of tweets propagating misinformation about two vaccines: the COVID-19 vaccines and the Human Papillomavirus (HPV) vaccines. Misinformation targets are organized in vaccine-specific taxonomies, which reveal the misinformation themes and concerns. The ontological commitments of the Misinformation taxonomies provide an understanding of which misinformation themes and concerns dominate the discourse about the two vaccines covered in VaccineLies. The organization into training, testing and development sets of VaccineLies invites the development of novel supervised methods for detecting misinformation on Twitter and identifying the stance towards it. Furthermore, VaccineLies can be a stepping stone for the development of datasets focusing on misinformation targeting additional vaccines.