Is there a way to drop a lit torch in my house?

Highlight it in your inventory and then press (X) to drop it, it will automatically be lit.

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.

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.

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.

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.

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.

If playing on the PC or Xbox One, there's a mod that allows you to drop lit lanterns and place them wherever you want: Wearable Lanterns (original / Legendary Edition - PC) / (Special Edition - PC) / (Xbox One).

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.

1. Drop all your torches but 6. (should be unlit)
2. Equip a torch
3. Drop the remaining 6 torches as well. (Should be lit, and in a pack of 6 torches)
4. Pick the rest of the unlit torches from the ground.
5. 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.

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.