title said it CAN I?
You can do any technique at any time. What you mean is: “What are the chances of success by using the mnemonic induced lucid dream method when being tired ?”
Answer: Depends on yourself. For one the best time to do a technique may be when tired, while for others the best period for practicing a method is while wide awake during a day nap.
It’s easier to do methods when sleepy, because sometimes the rollover signal is very weak or inexistent and everything is somehow faster. But you can’t keep yourself awake because you are tired.
So, if you ask me, I suggest to do any method when not too sleepy and not to awake. If you have problems with this (like I do), I suggest around 10:00 PM going to bed every night should fix this…