I brought a small Lavender plant home a couple of weeks ago. It was doing great until a couple of days ago. Right now, the leaves are curling in all directions and slowly turning brown. I currently water it once a week but mist the leaves daily.

If it's anything like my indoor lavender it will need more watering than once a week. The potting mix looks dry in your picture, can you tell if that's correct? I would stop misting it. It's a dry climate plant and doesn't need misting. If the potting mix is very dry you may need to soak it in a tub to rehydrate the rootball. I'm assuming it is not overwatered based on appearance and that it's been watered once a week. Did you also repot it?

Misting essentially does nothing. It causes a small localized increase in humidity and that is brief at best.
It looks to me that the plant has succumbed to not enough water. Every part of the plant looks to be suffering from being under watered.
Soil should be evenly moist, not dry, not soggy either.
Welcome to the forums and I am sure others will offer opinions as well.

Lavender grown in perfect conditions with perfect watering often dies quickly in kitchens indoors ..
not the easiest of herbs to grow indoors .

easy to grow in the summer in full sun with good drainage