Hi, 
what do you mean by "  if there is already an account, the lead should only be converted to Contact and if there is no Account "?
From what I understand from your question, if the Lead is already associated with an account, then you want the lead to be under the related account if not then convert it into a new account and Lead.
IF this is right, then
try this code for the Lead Conversion but still, you will need a field that connects the account to lead, see if you already have one, for the time being, we will call it 'accountid__c'

public static map< id,id> mapAccount = new map<id,id>();
for(Account a : [select id from Account])
{
     mapAccountount.put(a.id, a.id); 
}
list<Database.LeadConvert> MassLeadconvert = new list<Database.LeadConvert>();
     for(id currentlead: LeadIds)
     {
         if(mapAccount.get(currentlead.accountid__c) != NULL)
         {
            Database.LeadConvert Leadconvert = new Database.LeadConvert();
                Leadconvert.setLeadId(currentlead);                
                Leadconvert.setConvertedStatus(CLeadStatus.MasterLabel);
                Leadconvert.setDoNotCreateOpportunity(TRUE);
                Leadconvert.setAccountId(mapAccount.get(currentlead.accountid__c));
                MassLeadconvert.add(Leadconvert);
             
         }
         else
         {
            Database.LeadConvert Leadconvert = new Database.LeadConvert();
                Leadconvert.setLeadId(currentlead);                
                Leadconvert.setConvertedStatus(CLeadStatus.MasterLabel);
                Leadconvert.setDoNotCreateOpportunity(TRUE);
                MassLeadconvert.add(Leadconvert);
         }
      }

      if (!MassLeadconvert.isEmpty()) {
            List<Database.LeadConvertResult> lcr = Database.convertLead(MassLeadconvert);
        }