sounds like you have it figured out for the most part. poor diet, lack of exercise and bad sleep habits will cause depression, even if you have nothing to be depressed about. also, a lazy life is depressing. period. food for the body is like gas for the car. stay properly hydrated and eat healthy food and enough food all day long and i guarantee you'll have more energy. i can watch my body start to fatigue and want to shut down when i don't eat. it starts with hunger, the hunger starts to subside into stomach discomfort, then it turns into tiredness and i just want to sleep. im not a nutritionist so i don't know exactly what you need, but protein and carbs are going to be your best friend if your active. oh and i bet you'll notice a huge difference in just staying properly hydrated all day.
a lack of exercise will do it too. if you don't use it you lose it. muscles atrophy, endurance fades. you have to continually push yourself to the next level if you want to increase your strength and endurance. if you don't eat right and get no exercise then your body probably gets exhausted from just carrying its own weight around all day. exercise benefits not just the body but the mind as well. it causes the natural release of endorphins which will help with your depression.
lastly its not all physical. even if you eat healthy and get plenty of exercise you can still be mentally lazy. focusing mentally on something is only going to make you crave it more. i do it to- somedays when i wake up at 4 am to go to work all i think about for the first 2 or 3 hours im conscious is SLEEP, and how badly i want it. somedays i will sit and fantasize about sleep. it makes me groggy and lazy. try telling yourself to "wake the fuck up and stop being lazy". it works for me if i really listen to myself. instead of thinking about sleep, about how fatigued you feel, and how nice a nap sounds, think about things that you need to get done, things that you want to get done, things that will improve your well-being. if you really need sleep, don't deny your body but know that everytime you are tired does not mean you need sleep. it might just mean your bored and you need more stimulation. go out and be alive instead of curling up in your bed.
hope things are getting better for you. i share the same struggle. i used to sleep in until 5 or 6 pm everyday, got about 12-14hrs of sleep a day, ate like shit, got no exercise and couldn't figure out why i was so fucking depressed and tired all the time..lol. my family sounds alot like yours as well. i think our problem is rooted in bad habits more so than bad genes. at some point you have to break the cycle, and start taking care of yourself. for me, i landed a job in construction so i was forced to kick start myself. had to start waking up at 4 am and working 10-16+ hr days. at first it was killing me, but i stuck to it, took my own advice and i feel alot better now. just push yourself, you'll be surprised what you can do.