Variety is the spice of life. Our personal taste causes us to recommend that you not paint grasscloth, but rather brighten it by slowly and carefully vacuuming the entire surface. But if you must paint, you may elect to use either oil or latex paint with certain cautions: 1) use a flat (not shiny) finish, 2) thin the paint (2 parts paint to 1 part thinner or water) and 3) apply the paint with a sprayer in very thin applications.
Painting with a high gloss paint will tend to accentuate unattractive irregularities in the grass cloth that otherwise add to its beauty when it is in its natural state. Thick paint will fill in the narrow spaces between the straw, and may ruin the look you are trying to achieve. Use very thin layers of paint checking the result after each layer dries to ensure you get the effect you want. Applying wet coat over wet coat is not recommended for two reasons: the net affect of paint can't be determined until it dries and getting the surface too wet may de-laminate the paper from the wall.