Lithium Hydride is a hydrogen-rich compound with potential application as fuel, thanks to its high density and low molecular weight. It reacts exothermically with many substances and contains H2, suggesting its use where a much higher density (compared to that of LH2) would be beneficial. In this work LiH (solid at STP) has thus investigated as potential candidate for solid fuelled scramjets (SFSCRJ). Its thermochemical properties and issues associated to its combustion in a hot supersonic stream have been investigated; results show clearly that Li, released by thermal decomposition, plays a key role in the LiH performance. In fact, above the auto-ignition point liquid Li combustion with air increases local temperature and promotes LiH decomposition. To understand quantitatively these effects, a simplified physical model describing LiH "vaporization" and combustion was built and used in simulations of a notional SCRJ chamber by means of a CFD code. Results are intriguing: an intense and stable flame zone is predicted to be present over and downstream of the grain and high temperatures (of order 2900 K) are obtainable. Moreover, specific impulse and thrust density predicted at a flight Mach = 7 are also interesting, being 10,000 m/s and 200-300 m/s, respectively.