You hired Lydia as house steward for Heljarchen Hall I presume? You could try visiting during the day, and hang around the house for a while and watch who comes comes in the doors at night, but be quick, Lydia will be in a hurry to rush off for a drink at the local meadery. Do not expect that house to be furnished any time soon. And furnishing it yourself will make no difference, she will still furnish in her own time, whether you built it or not, so do not store anything in any of the containers. When she builds them they will be replaced.
Lydia will sometimes teleport back to the house during the day, but if you cannot catch her, try a short fast travel and return. She should return to the house for a few minutes when she should be going to sleep, but she will promptly rush of on her nocturnal travels to the meadery. The longer you spend at the house, the more likely your tipsy steward will be forced to make an appearance, but still do not expect any furnishing any time soon, she is too tired.
If you absolutely get desperate for a furnished house you can use, become Thane and get the housecarl, save your game at the house, and make sure to keep that save. Kill Lydia make the housecarl your new steward and ask him to furnish the house, you should not need to pay any extra. When the house is furnished, save the game, then reload your previous save with Lydia still alive if your house is not furnished it should be soon, maybe travel away a short while to give her time to settle after her trip to the twilight zone. If it does not work you will be no worse off, you can keep Lydia or return to a furnished house with a Lydia dead. Make sure to do all that in one playthrough, no exiting the game. if you are lucky enough to end up with a furnished house and live Lydia, save! But do not over write either of those previous saves till you are absolutely happy with the result. It worked for me on the Xbox 360, and I actually missed a few things in the entryway which is the only thing I asked her to furnish, she did put the rest of the animal trophies in there in record time. And she stayed around the house a bit more.
I actually killed Lydia because I was sick of her slacking off and wanted that entryway furnished, then after I had finally seen what it looked like with the door mat and bench, felt guilty and reloaded my previous save to get Lydia back. I was surprised to find I got to keep the furnishings, and that Lydia actually did a bit of work for a change. Pretty sure she has never slept at Heljarchen Hall though, she never sleeps, but still does her nightly dash to try and get to the meadery.