Write Something Lethargic
Often, the key to getting something to sound lethargic is to get your arms and fingers to mimic how it feelsto be lethargic. Lazily sliding from one note to the next, arriving to your notes late, playing behind the beat as if the drums have to pull you along - these are all ideas.
Explore, have fun, and try your hardest to write something with some lethargic elements to it. When you feel like you've got something - wether it's a VERY simple chord progression, a melody, or a full blown song, post it to the community forum.
Remember, not everything you write needs to be a complete song, not everything you write needs to be finished, and not everything you write needs to show people who you are. This is just practice. Have fun with it!