"할 말을 잃다." literally translates to
(Subject) loses (잃다) words (말) to say (말하다).
"할 말을 잊다." is literally
(Subject) forgets (잊다) words (말) to say (말하다).
Both sentences sound very confusing as in
그가 한 짓은 나에게 할 말을 잃게 / 잊게 만들었다.
(Literally) What he did made me lose / forget words to say.
Is there any difference in their meaning and usage?