Auxin is a plant growth hormone primarily known for its role in stimulating plant growth by facilitating elongation of cells within shoots. Its effect varies depending on the plant species and its developmental stage. The given options can be assessed to understand why grass remains undamaged in lawns treated with auxin for weed control.

Option A: promotes apical dominance.
Apical dominance refers to the phenomenon where the main, central stem of the plant grows more dominantly than the side stems due to the concentration of auxin in the apex. This is not relevant to the selective action of auxin on weeds versus grass, because while it might affect growth patterns, it doesn’t relate directly to why weeds are eliminated and grass is not.

Option B: promotes abscission of mature leaves only.
Abscission is the process where parts of a plant, such as leaves or fruit, are shed. Auxin helps delay abscission by inhibiting the process. Thus, promoting abscission does not align with the characteristic actions of auxin. Additionally, this mechanism would not be selective for weeds over grass.

Option C: does not affect mature monocotyledonous plants.
Grasses are monocotyledonous plants, characterized by having one seed leaf, parallel leaf veins, and vascular bundles scattered in stem sections. It is known that the structure and growth patterns of monocots differ sufficiently from dicots; hence, many dicot-specific herbicides (including those based on auxin-like substances) do not affect monocots. Therefore, this option provides a plausible explanation why grass, a monocot, remains unaffected by a treatment intended for dicot weeds.

Option D: can help in cell division in grasses, to produce growth.
While auxin does promote cell division and growth in plants, this is a generalized action and does not explain why it would selectively not harm grass when used as a weed killer in lawns.

Based on the analysis above, the correct answer is Option C: does not affect mature monocotyledonous plants. This option directly addresses the differential effect of auxin on monocots versus dicots, aligning with the observed outcome that grass remains undamaged while dicot weeds are targeted.