Is it safe to boil lemon water?

To make the house smell like lemons, a better way might be to bake leftover lemon rinds (whole lemons work too, but the rind is really all you need) on a foil-covered baking sheet. I occasionally do this with oranges and cinnamon sticks. Bake them at around 250 or 275 degrees (F). Bake them until they turn dark brown and start to smell toasted.

Yes, that's safe. I don't know if it'll really make the house smell that strongly, but yes, you can safely boil (or otherwise cook) any food you want, especially if you're not even going to drink or eat it. (Yes, there are exceptions like oil and alcohol, but anything you'd actually eat or drink in large quantities is fine.)

Food safety issues are generally things like "that meat has bacteria so you need to cook it thoroughly" or "you left that food out too long so it's not safe anymore." It's not really a safety issue to cook something in the first place, unless you're doing something that'll start a fire or something.

I suppose if you're going to leave this boiling so long that the pot cooks dry, that'd at least mess up your pot and conceivably could be a fire hazard. So don't, say, start it boiling then leave the house for hours and hours. But yes, boiling water is safe.