Sorry to disappoint but the disposal is not a small appliance in the NEC sense and it can be wired with 14 AWG, and yes you can run the lighting and the disposal together.
210.23(A) 15- and 20-Ampere Branch Circuits. A 15- or 20-ampere branch circuit shall be permitted to supply lighting units or other utilization equipment, or a combination of both, and shall comply with 210.23(A)(1) and (A)(2).
A small appliance is a something that is allowed to be fed from the small appliance branch circuit, you may not feed a disposal with the small appliance branch circuit.
A disposal is utilization equipment fastened in place and as long as it meets 210.23(A)(2) it is allowed to be on with the lighting circuit.
[210.23(A)(2) Utilization Equipment Fastened in Place. The total rating of utilization equipment fastened in place, other than luminaires (lighting fixtures), shall not exceed 50 percent of the branch-circuit ampere rating where lighting units, cord-and-plug-connected utilization equipment not fastened in place, or both, are also supplied.
Question, what is the electrical safety hazard by having the disposal on with the lights?
(A) Practical Safeguarding. The purpose of this Code is the practical safeguarding of persons and property from hazards arising from the use of electricity.
(B) Adequacy. This Code contains provisions that are considered necessary for safety. Compliance therewith and proper maintenance will result in an installation that is essentially free from hazard but not necessarily efficient, convenient, or adequate for good service or future expansion of electrical use.
The great thing is we can always choose to go beyond code minimums, I would run a separate circuit but I am not required to.