需要用到​​INNER JOIN​​。

UPDATE `table_live` a
INNER JOIN (
  SELECT
    GROUP_CONCAT(c.id) AS group_ids,
    ingroup
  FROM
    `table_live` c
  WHERE
    ingroup = 11245
) AS b ON a.id = b.ingroup
SET a.groupliveids = b.group_ids
WHERE
  a.id = 11245;

参考：https://dev.mysql.com/doc/refman/8.0/en/update.html