LINQ Join with Multiple Conditions in On Clause

Here you go with:

from b in _dbContext.Burden 
join bl in _dbContext.BurdenLookups on
new { Organization_Type = b.Organization_Type_ID, Cost_Type = b.Cost_Type_ID } equals
new { Organization_Type = bl.Organization_Type_ID, Cost_Type = bl.Cost_Type_ID }

You just need to name the anonymous property the same on both sides

on new { t1.ProjectID, SecondProperty = true } equals 
   new { t2.ProjectID, SecondProperty = t2.Completed } into j1

Based on the comments of @svick, here is another implementation that might make more sense:

from t1 in Projects
from t2 in Tasks.Where(x => t1.ProjectID == x.ProjectID && x.Completed == true)
                .DefaultIfEmpty()
select new { t1.ProjectName, t2.TaskName }