Metaphor or idiom?

It's neither.

'a big lift' is just standard speech.

A metaphor is defined as:

A figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable.

a big lift does not fit here because it is literally applicable -- moving the bed will presumably be a big lift.

An idiom is defined as:

A group of words established by usage as having a meaning not deducible from those of the individual words

Definitely not this - the meaning is indeed deducible from the context.

I say it's standard speech. Highlighting the aforementioned phrase- Moving the bed will be a big lift, you can just see that it's a statement where the adjective big just describes the action of the lift.

If you were talking about weightlifting as a sport, it would be an idiom, as John Lawler has pointed out. But out of that context, it's just plain English.

Hope this helps!

Both [1] [2] definitions from Oxford Dictionaries.