Does dilithium exist?
The dilithium dimer exists- but it isn’t particularly common, and we usually only see it in the gas phase. 

Essentially, the 2s electrons interact and form a bonding orbital. (s-p mixing is particularly pronounced here, but I presume you don’t know MO Theory.)

Due to the diffuse nature of lithium’s atomic orbitals, the bonding is pretty weak (Wikipedia gives a binding energy of $102\text{ kJ/mol}$, about one fourth that for a hydrogen molecule); and the inter nuclear distance between the 2 lithium atoms is actually quite large.