Ran into an interesting recommendation on fighting a lithium fire in Joshi, D.K., et al, Organic Process Research & Development, 2005, 9, 997-1002.
In addition to the usual admonitions on the handling of a reactive metal like Li, they warned that water, sand, carbon dioxide, dry chemical, or halon should not be used. Rather, they suggest dry graphite or lithium chloride instead. This seems quite reasonable to me, having reacted both silica and CO2 with magnesium powder in chemical demonstrations in a previous life. If Mg will reduce SiO2 and CO2, then hot/burning lithium ought to be reactive as well.
A similar recommendation is given in Furr, A.K. CRC Handbook of Laboratory Safety, 5th Edition, p. 299, ISBN 0-8493-2523-4.