What are the conditions for liquid metal to be corrosive to another, different solid metal?
There are no general conditions- indeed there no general conditions for the any of the forms of corrosion. Solubility is a factor and many other factors but it just comes down the actual interactions between a given liquid metal and another metal and the service conditions such as temperature, velocity, impurities. 

Liquid-metal attack has the following categories:


simple solution,
alloying between liquid metal and solid metal,
intergranular penetration,
impurity reactions, 
temperature-gradient mass transfer,
concentration-gradient mass transfer, or dissimilar-metal
mass transfer. 


With that many means- determining what liquid metal damages what solid metal  is very difficult.

http://web.ornl.gov/info/reports/1956/3445603500959.pdf