Here are some tips:
Train with low reps and heavy weight in the morning.
Train one or two body parts twice in the same day.
Train to get a pump in the evening.
Save at least 4 hours between the morning and evening workout.
These are certain ways that will help you to lose weight and will maintain strength.
Eat Enough Protein
Reduce Weight Training Volume and/or Frequency
Get Pre & Post Workout Nutrition Right
Don’t Reduce Calories By TOO Much
Take Diet Breaks When Needed
Stop cycling for few days and start noticing that whether you can sleep better after leaving it or not. I think cycling is the main issue behind your problem.