Methods of mitigating lost circulation while drilling a wellbore. The methods include circulating a drilling mud to a downhole end of the wellbore via a drill string and, during the circulating, drilling the wellbore with a drill bit of the drill string. The methods also include detecting lost circulation within the wellbore while drilling the wellbore and include providing a monomer solution to the wellbore. The methods further include providing a catalyst to the wellbore responsive to detecting the lost circulation event and combining the monomer solution and the catalyst to polymerize a monomer from the monomer solution, within the wellbore, and forming a viscous plug within the wellbore. Subsequent to the combining, the methods include flowing at least a portion of the viscous plug within the wellbore and into a zone of lost circulation that extends within a subsurface region. The methods further include at least partially occluding fluid flow from the wellbore and into the zone of lost circulation with the viscous plug.