1. I cannot speak for TEP/Silicone sex dolls, but I can speak for fleshlights. I tried using things other than lube and ended up ruining them quite quickly. Plus it does not feel well entering the body.
2. Any toy that states it can be cleaned with soap and water should not be damaged by soap. Hand soap is used as a lubricant by a lot of men in the shower. But can cause irritation and sensitivity to the inner penis owing to soap taken in through the urethral meatus of the penis (opening at the end). Glycerin-based soap is popular. Avoid deodorant-style soaps. As to the doll or sex toy, research the materials they are made of to ensure soap will not inure them.
3. Lube up, water-based lube is the best choice. You don’t want to hurt yourself humping dry rubber, or using products like Vaseline or lotion that could have harmful effects on your privates over time. Lubes are not that expensive. You don’t need a lot of it and it’s worth every penny in the long run. Lube is designed for sex/masturbation, so in my opinion, use it, because that’s what it’s for.
4. Use water-based lube. Do not use soap unless you really love a burning sensation when you pee. Look in the pharmacy aisle of basically any large grocery store they will have bottles of lubricant, it will be under random names but it will say something like “water-based personal lubricant” in small letters on the bottle.