If a mutation introduces a new skin color in a lizard population, which factor might determine whether the frequency of the new allele will increase

The answer is: It will depend whether this mutation will make those lizard more fit than the others.

Genotype variations that will increase the chance of survival and reproduction of some organism are preserved and will be inherited. Fitness describes a reproductive success of an individual. For example, there are green lizards in a population. After a mutation, there are now some yellow lizards in population. If a color affects the reproductive success, for example, yellow lizards will have more offspring, and their allele will be inherited. So, the frequency of the new allele will increase.