I can't vouch for the rest of the country, but in California almost every wildland fire agency uses an automatic dispatch with a CAD most of the time. This is a complex system based on the experience of fire managers, data from the field, and the availability of resources. Areas are drawn with similar access, fuel type and loading, structure threat, and resource values. Each day the dispatcher enters current staffing, and fire danger into the CAD. Fire danger is derived from burning index, spread component, ignition component, energy release component; 10, 100, and 1000 hour fuel moisture readings taken the previous afternoon as well as predicted wind speed and direction, predicted humidity and precip., and human caused fire risk (higher on holidays when visitation is up, etc.). This is the quick version as there are some things I haven't mentioned and some I won't try to explain such as the various hour lengths for fuels. When a fire is reported it is located within an area and the resources dispatched to it are based on all the factors I've explained above.
This is not a static system as fire managers meet at least annually and tweak the plan based on experience. They try to get rid of problems such as having five engines, two water tenders, three dozers, four crews, two helicopters, air attack, a lead plane, and three heavy air tankers being dispatched to a 100 acre grassy area that is surrounded by an equal or greater amount of rock with a one acre fire burning in it. The system was put in place to avoid potiential delays caused by decision making for each fire start. Such decisions, even when made by very experienced managers, can be difficult to make and include all the factors in the first paragraph. Automatic dispatch works best with single start or low number of fire starts are occuring. Human caused fires are somewhat predictable when compared to lightning as they tend to start, most of the time, in places that are no surprise to people who have worked in an area for many years.
Now when lightning begins to strike, automatic dispatch has a great deal of trouble considering all the variables that come into play during thunderstorms. What are these variables? Wind direction and speed during different stages and movement of thunderheads, wetting rains over some reported fires and none over others, starts in places that are not as easily predicted as human caused, varying relative humidity levels over wide areas, and multiple starts, and some all by themselves and some closely spaced together, are some of these variables. Anohter big factor is the false alarm rate during thunderstorms is quite high as untrained observers call in clouds, water dogs, dust, and the like. Water dogs are water vapor in very small clouds (we are talking about something about the size of a 3/4 ton pickup or smaller) located near the tree tops of trees and ridges and ground surface. They look just like a smoke rising. With years of experience one can usually tell the difference from distant observation locations. During such periods it becomes necessary to make resource assignments based on the situation that presents itself right then. In that way the most intensely burning fires, in the areas with the highest resource values and greatest structural threat, can be assigned resources in a priority fashiion.
Decsions to fully staff a single tree fire while leaving fires of several thousand acres unstaffed can be made. Although this is an extreme example, I saw it happen during my career during the late August, early September 1987 lightning bust in cental/northern California. If there are not multiple starts and you have a few strikes from "dry lightning" you might hear fire managers decline to put a jurisdiction into lightning plan, and when a lightning fire starts they may ask for a full response.
The person who coordinates resource allocation during lightning events is usually very experienced with the local area and has sufficient fire qualifications to make decisions, which at times, can be difficult to make. Sometimes you really don't have good alternatives, just a hand wringing process to come up with the alternative with the fewest and "correct" negatives. This person can be the Division Chief (Fire Management Officer in USFS lingo), a battellion chief (assistant fire mangement officer, fuels batt officer, prevention batt officer), a crew or helitack superindentant, engine captain, or patrol (fire prevention technician or FPT in USFS lingo). It depends on how many fires are active locally, regionally, and nationally and what the local jurisdication is experiencing as far as draw down (resources assigned off of the local area). I've seen District Rangers, recreation supervisors, resources staff officers, and similar assigned the title of "lightning coordinator" on given days depending on the conditions and the qualifications of those people. As a field supervisor in recreation I had higher wildland fire qualifications than the full time paid chief of our local fire department who had been in the fire business for 25 years, but in his case, mostly in structural protection some distance from any wild lands. Often the person's title does not indicate their qualifications.
What you often have during lightning conditions is more workload than resources, so the lightning coordinator is very much like the medical person in charge of triage on multiple casualty incidents and in hospitals. This person needs to be able to keep track of the big picture to make decisions that are best for all the patients, not just for each of them one at a time. It is best when this person is not caught up in the details of each patient. This is what a lightning coordinator does. It can't be an incident commander on one fire or a module leader (of a resource such as a hand crew, engine, etc.) as they would be influenced by the incident or module they are supervising. Since this person is drawn from a diversity of sources, the term "lightning coordinator" is the best term to describe what that person is doing.
Such wildland and all risk triage can occur when many large incidents are located in an area. When this happens "area command teams" are put in place to manage the resources assigned to a group of incidents so you don't have several incident commanders fighting with each other when dealing with the Geographical Area Coordination Center of with the National Interagency Fire Center in Boise. Area teams don't have many members and they don't get caught up in details, but must understand how those details affect the entire situation. I believe the current count of Type I National Incident Management Teams is 17, Type II teams is in the neighborhood of 36, with the number of Area Command Teams at around 4-6. Area teams are also used when the incident is so large that more than one Type I team is assigned. I could go on and on, but will stop here. My career involved incidents prior to the development of ICS and after. Up to the time I retired I was exposed to this stuff quite frequently both through experience and the required training. Fascinating stuff.