It is possible, yes, but it's definitely alot harder to forget lucid than non-lucid, especially if you are practicing and have done alot in dream. As long as you have stable enough recall, even if it's 1 dream/night(Hey, my recall was even worse when i was starting), it's good to Not worry that much and practice lucid dreaming as well, both will improve!
The only instances when i've found recalling lucid hard personally is when i had massive chains of false awakenings, other than that my recall of lucid always was pretty clear, even when i was starting.
Be sure to check out threads NyxCC linked!

*Moved to General Lucid Discussion*