Lead Convert Trigger to not create new account but use and existing account.

I am using a trigger to fire on my web to lead form from a specific leadsource to create a contact. Is there a way for it to not create an account but add the contact to and existing account? here is my code. what I am thinking is that I would create an account trigger to fire on the leadsource and add the contact to the account correct??

here is the lead trigger:

trigger KYR_LeadConvert on Lead (after insert,after update) {
List<String> LeadNames = new List<String>{};
for(Lead myLead: Trigger.new){
if((myLead.isconverted==false) && (myLead.LeadSource == 'youknowit')) {
Database.LeadConvert lc = new database.LeadConvert();
        lc.setLeadId(myLead.id);
        lc.setopportunityName(myLead.Refersite__c);
        lc.convertedStatus = 'Qualified';

        //Database.ConvertLead(lc,true);
        Database.LeadConvertResult lcr = Database.convertLead(lc);
        System.assert(lcr.isSuccess());
        }
        }
}

thank you for the help;)