No need for JOIN LATERAL (or do you really just want to use it?); an UPDATE will pass each rows SET value to the following query, which is the same concept as using a JOIN LATERAL.[*]
Try
UPDATE gps
SET stop_id = (
SELECT stop_id
FROM stops
ORDER BY gps.geom <-> stops.geom
LIMIT 1
);
*You are a very experienced PostGIS user; still, let me add some notes on distances and the KNN operator ,)*
In my experience, for points the `` operator tends to perform even slightly slower than with plain old `ST_Distance` (check if the index scan actually kicks in with ``). For better precision, consider casting to geography; the `` operator then measures on a sphere, while `ST_Distance` uses the actual spheroid.
If the tables are massive, you can add a `WHERE ST_DWithin(gps.geom, stops.geom, )` to only compare those `stops` in each `gps` points' vicinity (note that the distance given uses the CRS units (i.e. degrees for *EPSG:4326*) for *geometry*, but meter for *geography*).
[*] Just to give an example on that; consider a `SELECT` instead to find the closest `stop` to each `gps` point using `JOIN LATERAL`:
SELECT a.gps_id,
a.measured_timestamp,
a.geom,
b.stop_id
FROM gps AS a
JOIN LATERAL ( -- you can use 'CROSS JOIN LATERAL' without 'ON true',
SELECT stop_id -- but I get slightly faster results this way
FROM stops
ORDER BY a.geom <-> stops.geom
LIMIT 1
) AS b
ON true;
Each row in gps is now passed individually and subsequentially to the JOIN LATERAL sub-query to be processed; this (sort of) mimicks the UPDATE command (note how it is the same sub-query).