[Aakash]

Why does hydrogen form metallic hydride like LiH when both the metals want to lose electrons?

[Corribus]

You are anthropomorphizing too much.  What makes you think they want to "lose" electrons?

[Hunter2]

Hydrogen is able to get the noble gas shell from Helium with two electrons. So it is possible to form Hydrids. Like LiH, CaH₂, etc.

[Enthalpy]

No atom loses electrons easily, because the resulting positive ion attracts electrons.

An electron transferred from one atom to an other can happen in a strict ionic bond, when one atoms attracts the electron much more than the other does - AND it needs some mechanism to help the resulting ions keep stable.

In a solid, positive ions are closely surrounded by many negative ones (and negative by many positive ones) so that the electric potential of the ions is not too big.

In a polar solvent, liquid molecules put the end of opposite charge near each ion, which again reduces the electric potential.

Other bonds - which can be strong as well - rather put electrons of both atoms on a new common orbital, which can be more favourable than the separate atoms. And since most atoms are already bound in molecules (H₂, O₂, N₂...) a reaction has to break the old molecules first, so it's a mere re-arrangement of the bonds.