Apparently LogParser v2.2 (latest version unfortunately) doesn't support JOIN operations.
I've seen a few samples on the internet that suggest ways to try and simulate a JOIN. One used a IN operation with a sub-query in the WHERE clause:
SELECT * FROM Log1 WHERE FieldA IN (SELECT FieldA FROM Log2)
That may be sufficient for what some people need JOINs for - filtering. But if you want to see data from two different sources on the same line - that's not going to accomplish it.