1. Lovers can't have everything easy all the time.

2. Lovers can't have everything easily all the time.
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Which one is grammatical? Are both ok? Do we have to use 'easy' or 'easily'?

The expression is "have it easy."

similarly expressions:

Some like it hot.
I can't get it right.

Using "easily" would indicate the having, rather than what is being had. (Also, I've never heard anyone say it!)