Why is the bond LiBr covalent?

LiBr bond is NOT covalent.

It is an IONIC Bond.

Lithium metal ionises one electron to become the lithium cation

Li = Li^(+) + e^(-)

Bromine has an electron affinity and absorbs one electron to become the bromide anion.

Br + e^(-) = Br^(-)

The two ions have the same charge of '1' but of opposite characteristics. (+/-).

By mutual attraction, named electrostatic attraction, they come together as an IONIC bond.

Li^(+) + Br^(-) = LiBr(s)

Think of it a like the N & S poles of a magnet.