I purchased Lakeview Manor and built my house upon the property and asked Lydia to be my steward. Whenever I ask her to furnish a room the money gets exchanged but the room doesn't get furnished. Whenever I ask her to furnish the entrance it will give her the 1000 gold but the room won't get furnished and the option is still available but she says something like "hmmm, you don't have enough to purchase that" or whatever. Any tips would be greatly appreciated.

From the UESP wiki:

Bug: Personal stewards may tell you that you don't have enough gold when you attempt to furnish rooms, even when you do. This is usually caused by furnishing a room before asking the steward to do it.

Also, keep in mind that it can take some time before your steward gets around to furnishing your home; it doesn't happen immediately. Try coming back to your home after 10 (in-game) days and see if she has gotten around to furnishing it yet.

If all else fails, you can gather all the materials on your own and build the various furnishings yourself at the workbench.