var results = (from g in _groups
                     join cr in _categoryRoots on g.Id equals cr.Group_Id into gcr
                     from lgc in gcr.DefaultIfEmpty(new CategoryRoot())
                     join c in _categories on lgc.Id equals c.CategoryRoot_Id into ccr
                     from lccr in ccr.DefaultIfEmpty()
                     select new GroupCategory
                     {
                         Id = g.Id,
                         Name = g.Name,
                         CategoryRoot_Id = lgc == null ? 0: lgc.Id,
                         CategoryRootName = lgc == null ? "": lgc.Name,
                         Category_Id = lccr == null ? 0: lccr.Id,
                         CategoryName = lccr == null ? "": lccr.Name
                     }).ToList();

var rs = _groups.Join(_categoryRoots, g => g.Id, cr => cr.Group_Id, (g, cr) => new GroupCategory { Id = g.Id, Name = g.Name, CategoryRoot_Id = cr.Id, CategoryRootName = cr.Name  });

var results = (from g in _groups
               from lgc in _categoryRoots.Where(cr => g.Id == cr.Group_Id).DefaultIfEmpty(new CategoryRoot())
               from lccr in _categories.Where(c => lgc.Id == c.CategoryRoot_Id).DefaultIfEmpty()
               select new GroupCategory
               {
                   Id = g.Id,
                   Name = g.Name,
                   CategoryRoot_Id = lgc?.Id ?? 0,
                   CategoryRootName = lgc?.Name ?? "",
                   Category_Id = lccr?.Id ?? ',
                   CategoryName = lccr?.Name ?? ""
               }).ToList();