As already mentioned, there are daylight lamps out there, particularly fluorescents. Daylight balanced florries with a high CRI (colour rendering index) might be your best option.
Incandescent lamps lose about two stops when filtered to daylight with a gel (a full CTB) so it is quite common to filter the windows instead (full CTO or CTS depending on your preference). That makes it much easier to get the balance between the daylight and the artifical light. If you used tungsten film you wouldn't need a filter on your lens.
As you are using the window as a source of light you don't have to be as careful filtering it as you would have to be if the window was in shot.
If you want to use incandescent lamps filtered to daylight, dichroic filters would be better than gel ones because they lose less light and they last longer, but they are more expensive.
Best,
Helen