Can you LD during a sleep deprivation induced nap

A few weeks ago i was experimenting with sleep deprivation i stayed awake for a total of 90-100 hours and during the process i'd often have little micro naps where i'd lay down and drift of to sleep for a matter of seconds during which i often began dreaming. from what i understand to "lucid dream" you need to be in a light sleep i was wondering would it be possible to deprive my body of sleep for a few days and then take short naps like 20-30 mins and lucid dream?

It appears as if you answered your question before you asked it...
I'd say if it's possible to dream it's possible to lucid dream.

I have experienced not being able to LD, since my dream recall was off when I was not getting my usual rest.

I believe that you have the best dreams this way because of REM rebound that results from sleep deprivation. But take caution with sleep deprivation, dont use it as a method of inducing a lucid dream everytime.