Hmm where to start...
-Lamps make inadequate heat sources because you can't keep them on 24/7 or you'll drive your poor fish up the wall.
-A 1g bowl needs to be cleaned every 2-3 dyas to keep the ammonia a fish produces below toxic levels.
-Bettas are tropical fish and NEED a heater. In fact they prefer warmer water than most other tropical fish.
-Those feeder blocks are from the devil. Not only do they have the nutritional value of chalk (oh wait-they are chalk!) fish refuse to eat them and they will rot in the tank within days, polluting the water and poisoning your fish. I suggest you purchase a good pelleted
food like Hikari Betta Bio-Gold, HBH Betta Bites or Atisons Betta Pro.
-I suspect he is being so lethargic because of the cold temperatures. You can also help him by putting more plants in to make him feel at home.
And one more word... I was once a 'cheap' betta owner and kept my fish in a 1g bowl. That was until I found out that:
1) My bowl cost $16. I could have bought a 5 gallon tank, everything included for 4 bucks more.
2) I had to change the water every other day.
3) I literally could not find a single brand of heater that would heat such a small volume of water without cooking it.
4) I was spending more money on medicine to fix my fish (their immune system crashes in low temperatures and dirty water) than I would have if I just bought a freaking 5 gallon.
5) As soon as I released him into the 5g and watched him zoom around I wished I had bought a proper tank from the get-go!
This care sheet
is a good place to start for betta care fundamentals.
Good luck with this fish and welcome to the forum!