Pesticides may remain active for a month to a year or more. Even after drying, pesticides release toxic vapors. Insects shouldn't be a big problem in a natural lawn. Don't attack the insects that aren't doing damage to your lawn. Water during daylight hours.
Liquid seaweed is good natural disease fighter.
Naturally occuring hormones in seaweed act as fungal inhibitors. Despite the ads, most won't grow back if you cut them out several inches below ground at their root. High mowing combined with heavy fertilization eliminated crabgrass in just one year. Mowing correctly can kill weeds, save water, cure diseases and provide fertilizer. By mowing high, you're reducing stress on the grass.