When lead is created or updated then check if the email of lead is already there in existing contacts. If email already exist then throw an error.

Trg_CheckLeadEmail

trigger Trg_CheckLeadEmail on Lead (before insert,before update) {  
if(trigger.isBefore  && trigger.isInsert || Trigger.isUpdate))
{
    Trg_ClassCheckLeadEmail.CheckEmail(Trigger.new);
  }
}

Trg_ClassCheckLeadEmail

public class Trg_ClassCheckLeadEmail {
 public static void CheckEmail ( List<Lead> newLeadList){
    Set<Id> conIds = new Set<Id>();
     for(Lead l : newLeadList)
     {
       conIds.add(l.WhoId);         
     }
    Map<Id,Contact> mapConlst = New Map<Id,Contact>([SELECT Id, Email FROM Contact where  Id IN: conIds]);
     for(Lead l : newLeadList){
         if(mapConlst.get(l.whoId).Email == l.email){
             l.Email.addError('Email Already Exists !!!');
         }
     }
  }
}