LEFT JOIN LATERAL can remove rows from LHS

Maybe I am misunderstanding how LATERAL is supposed to work, but my
expectation is that doing a LEFT JOIN should not remove rows from
the LHS.  I would expect all of the following select queries would
return a single row, but that isn't the case:

CREATE TABLE i (n integer);
CREATE TABLE j (n integer);
INSERT INTO i VALUES (10);
SELECT * FROM i LEFT JOIN LATERAL (SELECT * FROM j) j ON true;n  | n
----+---10 |
(1 row)

SELECT * FROM i LEFT JOIN LATERAL (SELECT * FROM j WHERE (i.n = j.n)) j ON true;n | n
---+---
(0 rows)

INSERT INTO j VALUES (10);
SELECT * FROM i LEFT JOIN LATERAL (SELECT * FROM j WHERE (i.n = j.n)) j ON true;n  | n
----+----10 | 10
(1 row)

SELECT * FROM i LEFT JOIN LATERAL (SELECT * FROM j WHERE (i.n = j.n)) j ON false;n | n
---+---
(0 rows)

Is the error in PostgreSQL or my understanding of LATERAL subqueries?

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Thanks,
Jeremy