Yes any circle member can request checklists items or projects, and every single role filler gets to decide whether a new checklist or project makes sense for them to take on, based on their interpretation of their role's purpose and accountabilities.
To decide whether that "makes sense", they have to consider whether that ongoing action or project would serve expressing the role's purpose or accountabilities (versus any other actions or projects they could take). If they think that "yes it would", then they have to take that action or project (and therefore add it to the circle's checklist or project board). If they don't, then they can be requested to define another action or project to express the role's purpose/accountabilities. And if that still doesn't address the need of the role who requested it, then in that case, the requester might have to bring that tension to governance in order to clarify the role's purpose and accountabilities.
Lastly, if it's already an activity that the role filler is doing or a project s/he's working on, then s/he has to give updates on it upon request from another circle member (and therefore add it to the circle's checklist or project board).
The Lead Link has no special authority around requesting actions or projects.
Hope that helps and is not too confusing! And great question by the way, thanks for asking