Trouble remembering dreams from earlier in the morning

Hi, me again! :D

I am getting okay-ish at remembering dreams, but the majority of dreams I am remembering are the ones from the late part in the morning, just before or as I wake up.

I tend to wake once or twice throughout the night - but I am not remembering any dreams at all around here. I might wake up after about six hours of sleep, and there's just nothing. And I have this feeling like I was just dreaming, but I can't bring anything at all to mind.

Is this going to hamper my ability to have lucid dreams?
Is there a way I can improve this?
Or, is remembering only one dream - and it being the last dream - going to be sufficient?