After reading this post properly (!) you can't have an order by because (accoring to Quick Reference)
DSNH109I E csectname LINE nnnn COL cc type CLAUSE NOT PERMITTED
Explanation: The type is INTO, ORDER BY, FOR UPDATE, , USING, LARGE, or
o A SELECT INTO statement cannot include ORDER BY, because the result
cannot be more than a single row.
So, Dick is correct you will need a Cursor as you are doing a SELECT INTO. This way you can have the ORDER BY.
But.... have you tried SELECT CUST_NMBR, MAX(LAST_UPDT_DT) and remove the ORDER BY, this way you'll get the latest last update date without a cursor. See if that works.