Well, the companies selling fertilizers would have you believe that you need to do it 4-5 times a year :) I am not a biologist but it does make sense to me to fertilize the grass just before the season with the maximum growth so the nutrients are there when the grass needs it. That time will depend on your location and the types of grasses on your lawn.
There are two types of grasses: cool-season and warm-season grasses. You may live in the area where only one particular type will survive but a large swath of US territory (south of PA, north of SC and all the way west around those latitudes) can have both. Warm-season grass would turn brown in winter if it grows far enough to the north. Cool-season grass can be green all year round in the north and would have a tendency to wilt in summer in the transitional zone and would probably not survive summer in the southern states.
Cool-season grass needs early fall fertilizing most, when the summer heat has subsided and the grass is still growing. You can also fertilize in early spring before the summer heat comes and it stops growing again.
Warm-season grasses need fertilizing in the spring when they're becoming green after the dormant winter.Â
Make sure the fertilizer is gone (if it was in soluble granules) by the time the grass stops growing - it should be all consumed by the time the summer hear or the winter cold comes.
I'm mostly dealing with cool-season grasses myself and fertilizing is usually not during the time when watering is needed, so I don't use the liquid dispenser like you do. I have one of those push-type spreader carts. But if you're living in the region with warm-season grasses, I imagine the liquid dispenser can do the job just as well. If you have pets, using the liquid dispenser may be preferred so they don't pick up the granules.