Certainly! Here's a simple and effective lip scrub recipe that doesn't include coconut oil:

Ingredients:
- 1 tablespoon of brown sugar
- 1 tablespoon of honey
- 1 teaspoon of olive oil
- 1/2 teaspoon of vanilla extract

Instructions:
1. In a small bowl, combine the brown sugar and honey. Mix well until they form a thick paste.
2. Add the olive oil and vanilla extract to the mixture. Stir until all the ingredients are well combined.
3. If the mixture seems too dry, you can add a little more olive oil to achieve the desired consistency.
4. Once the lip scrub is ready, transfer it to a clean, airtight container for storage.

To use the lip scrub, simply take a small amount and gently massage it onto your lips in circular motions. This will help exfoliate dead skin cells and leave your lips feeling soft and smooth. Rinse off with warm water and follow up with a moisturizing lip balm.

Remember, it's always important to patch test any new skincare product or ingredient on a small area of skin to check for any potential allergies or sensitivities.