There is a bug, Have a living person holding a lit torch, then kill him while he is holding it lit.
The torch will be lit when he drops it and when you drop it, but make sure to kill him in one hit or he will put the torch away and draw weapons.
gaming.stackexchange.com/users/22515/Novastar
I've been experimenting with dropping torches (Don't ask), and it seems there is a bug.
The first time I dropped them, 69 were in an unlit stack and two more were lit and not stacked.
Picking them up and dropping them again caused them to consolidate into a stack of 71 unlit torches.
Try gathering more torches and see if some of them end up being lit upon dropping is the only advice I can offer.
gaming.stackexchange.com/users/19827/kotekzot
If playing on the PC, there's a mod that allows you to drop lit lanterns and place them wherever you want - Wearable Lanterns :
gaming.stackexchange.com/users/4797/galacticninja
Highlight it in your inventory and then press (X) to drop it, it will automatically be lit.
gaming.stackexchange.com/users/12721/JuniorDeveloper1208
Mine works like this: collect a load of torches, then when your ready to light some place up drop all your torches except for 6, then equip a torch and drop the last 6 and those 6 torches will be lit as one
, it wont work if you just equip a torch and drop 6 out of however many, because the torch in your hand wont count as one of the 6.
gaming.stackexchange.com/users/24683/Sean Hutchinson
Drop the unlit torches, leave your house for a period of time, and when you return they should be on the floor lit.
I dropped a ton in the Housecarl's bedroom and now it glows like the sun.
gaming.stackexchange.com/users/26683/flatlander five
Drop individual torches, (lit or unlit does not matter)
Place them where you want them to be, leave the building your house whatever, save the game then load the save, enter the house and they should all be lit.
gaming.stackexchange.com/users/47830/user47830
Even though the topic is 2 years old i found an easier solution that you don't have to enter or leave areas (or kill someone lol).
The drawback on this one is that it you need 6 torches each time.
Drop all your torches but 6.
(should be unlit)
Equip a torch Drop the remaining 6 torches as well.
(Should be lit, and in a pack of 6 torches)
Pick the rest of the unlit torches from the ground.
Profit.
Explanation
For some reason for this to work, when you have an equipped torch, it has to let you choose how many torches to drop in order to drop a lit one.
That is why you need to have at least 6 to trigger it.
Otherwise, (e.g. 5 or less torches in the inventory) you are going to drop each one individually.
gaming.stackexchange.com/users/77804/user77804
If you drop a torch on the ground, leave it for 5 real minutes, then use flames on it, it will put one or two ash spots before going away.
Do this about three times, go outside of wherever you are, go in somewhere, and it will be lit.
gaming.stackexchange.com/users/170901/yoyocraft1637
I dropped a torch in my house in whiterun and somehow it was lit. It was actually very helpful as it lit up dark areas of the house. Is there a way to make this happen again (on xbox)?I can't seem to make this happen again.
Is there a way to drop a lit torch in my house?
gaming.stackexchange.com
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gaming.stackexchange.com/questions/46945
gaming.stackexchange.com/users/16089/Bryan
There is a mod that allows you to drop lit lanterns and place them wherever you want. You can also just drop a torch, leave your house and then when you return they should be on the ground and lit. While it doesn't seem to be a clear way of dropping a lit torch, players have found different ways to do so.
The community is describing different  ways to do what has been asked.