int index = 0;

var workload = grouplist.GroupBy(j => new { j.LOGIN_ID, j.FULL_NAME,j.TEAM_NAME})

                .Where(k => k.Key.TEAM_NAME == membergroup)

                .Select(i => new

                {

                    CoreID = i.Key.LOGIN_ID,

                    TicketCount = tickets

                        .Where(k => k.Assignee_Login_ID == i.Key.LOGIN_ID   &&                      k.Assigned_Group==i.Key.TEAM_NAME)

                        .Count(),

                    Assignee = i.Key.FULL_NAME,

                    url = @"~\images\man_" + (1 + (index++) % 5) + ".png"

                }).ToList();           

I choose to use Lambda instead of Linq because of simplicity, Ill post another example using left outer join using Linq in the next one.