MySQL 5.7

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CREATE TABLE t (`name` VARCHAR(1) PRIMARY KEY, `value` INTEGER, `lastupdate` DATE);

INSERT INTO t (`name`, `value`, `lastupdate`) VALUES
  ('a', '10', '2021-01-01'),
  ('b', '20', '2021-02-01'),
  ('c', '30', '2021-03-01');

Records: 3  Duplicates: 0  Warnings: 0


INSERT INTO t (name, value, lastupdate) VALUES
  ('a', 20, '2021-01-01'),
  ('b', 40, '2021-01-01'),
  ('c', 60, '2021-04-01')
ON DUPLICATE KEY UPDATE
value = CASE WHEN VALUES(lastupdate) >= lastupdate THEN VALUES(value) ELSE value END;

Records: 3  Duplicates: 2  Warnings: 0


SELECT * FROM t;


name
value
lastupdate


a
20
2021-01-01

b
20
2021-02-01

c
60
2021-03-01