"Memories" is plural so you need the plural form of a verb.
The more natural way to say this is "These mememories will last a lifetime."
And by an amazing coincidence, there was a commercial for Disney World airing just now, and at the exact same moment I wrote those words, it said "memories that will last a lifetime."
Memories will last for a lifetime. Is this the only sentence we can use? Are there no any other alternatives? Please advice me what are the mistakes in the following sentences.
1. These memories stay/remain for lifetime.
2. These memories stay/remain lifetime.
3. These memories stay/remain through out the life.
Again, the natural one is "last a lifetime." If you really want to use your "remain," then "these memories will remain with you for a lifetime" or "... will remain with you throughout your life."
Not: - for lifetime - lifetime - for life long - life long