I define a profile where I deactivate the top options of see and use all and then all the modules except Accounts, Contacts and Leads.
Then I go to any Lead but the Convert Lead action is not there. Why?
I can only see the link if I activate see and use all, but then I also see al the modules, which I do not want.
I just tried and it worked correctly for me.
The problem must be with some field the conversion needs. I had a look at the code and it says that the "Convert Lead" action will be visible when all these conditions are met:
the user has edit permission on Accounts, Contacts and Leads
the user must have conversion tool permission in his profile (see image below)