Could liquid alkali metal fuels be used for ramjet/scramjet propulsion? In particular, I'm thinking about lithium, but sodium could be considered as well. 

Lithium has low molecular weight, very high propellant density, and low melting point. At sufficiently high temperatures (above 500 degrees Fahrenheit) it ignites spontaneously in air with explosive force. 

A lithium scramjet/ramjet would require an onboard power supply to heat the fuel to liquid and then pump it into the combustion chamber. The idea is that the combustion chamber would need to be hot enough so that the lithium droplets would quickly evaporate and ignite making the mixture hypergolic. 

I'm surprised that I have found no current R&amp;D into alkali metal fuels for rocket propulsion(let alone hypersonic propulsion). It seems to me that to make longer range hypersonic flight possible, exotic fuels will be absolutely necessary.
How long does the lithium take to evaporate and then to react with oxygen? Air in a scramjet is moving extremely fast (supersonic by definition!), so there is very little time left for mixing and combustion if you desire to create thrust from the the combustion heat energy.

Your lithium engine will most likely trail a bright contrail of burning lithium but develop rather little thrust. The high flame speed of a mixture of hydrogen and oxygen makes hydrogen the preferred scramjet fuel.