if lead email and contact email are matched then assign that lead to matched contact else assign that lead to primary contact using apex?

My requirement is,  

Convert Lead status as Joined based on Membershiphistory Begin date and lead created date. But Lead and Membership history does not have relationship. Lead and Member having lookup relation and member and membershiphistory having lookup relationship.

if lead email and contact email are matched then assign that lead to matched contact else assign that lead to primary contact using apex?

My requirement is,  

Convert Lead status as Joined based on Membershiphistory Begin date and lead created date. But Lead and Membership history does not have relationship. Lead and Member having lookup relation and member and membershiphistory having lookup relationship.