The user who invites a new participant (or the admin of the project) can give them access to the lists of his/her choice.
1) Open the participants menu in the entire project
2) Click on the manage icon on the top right corner
3) Click on list's rights
4) Click then on the edit icon on the top right corner of your screen, to be able to give the participant(s) of your choice access to some lists. Do not forget to save your changes!