Permanent compound modifiers (hyphen)

Hi

I know that compound modifiers are hyphenated when they modify a noun. There are however permanent compound modifiers such as "short-lived" that is always hyphenated whether it be followed by a noun or not. So to help oneself in identifying whether it is always hyphenated or not that advice is to check the dictionary.

I use Oxford dictionary so when I type long-term in the dictionary it shows low-grade as adjective and hyphenated. That would mean I should type long-term hyphenated all the time.

Is this correct?