Does thinking about lust while fasting, knowing that a viscous white fluid is discharged as a result, invalidate the fast and necessitate fasting for 60 days?

The viscous liquid that exits when thinking about things that arouse desire is madhiy (pre-seminal fluid), not maniy (semen). Maniy is what exits in spurts when desire intensifies. The emission of maniy or madhiy due to thinking does not affect the validity of the fast according to the majority of scholars.