"I am searching for a partner for life."
Translation:אני מחפשת בן זוג לכל החיים.
Is לכל החיים an expression that means "for life" even though it translates more literally as "for all of life"? Can you say "for life" without the כל? (I don't mean the toast "to life!")
You can. בן זוג לחיים is equally fine. I feel there is a small difference in meaning - בן זוג לחיים implies seriousness and commitment, בן זוג לכל החיים is more about never breaking up.
The phrase לכל החיים would be better translated to "the entire life", in this case. But as AlmogL said - yes, you can use your suggestion too