You can have a lucid dream at any time of the night (I think my earliest was after about 4 hours of sleep, approximately)...

BUT! The reason it's strongly encouraged to get 8+ hours of sleep is because the longer you sleep, the longer your REM periods become (REM is when dreaming happens).

It gets to a point that at that 8 hours of sleep point (I think it is), the chances of you being able to have a LD double vs. the previous 7 hours you just slept.

If you absolutely cannot get more sleep (ex. go to sleep earlier) on weekdays, you can try playing with some earlier WBTB ("wake back to bed." Get up, go to the washroom time, for most of us ).

Your WBTB needs to coincide with the end of a REM period, so you'll have to play around with the times. The best results are between 5-6 hours after you go to sleep for the night. If that doesn't leave you with enough time to attempt a LD, you can try 4.5 hours...