We ignore the 1s electrons, which are too close to the nucleus to contribute to bonding. We can make one bonding and one antibonding orbital from the two 2s atomic orbitals. The 2p orbitals allow us to make 3 bonding states and three antibonding states. Thus these two are degenerate by symmetry. Since each lithium atom has only 1 valence electron, we put the two molecular electrons into the lowest lying bonding orbital.
Beryllium is the next element in the first row.
Boron has two additional electrons to add. These electrons go into a bonding pi orbital, making the bond energy larger than that of Be2. The two additional electrons in carbon fill all the bonding pi orbitals. The bonding energy is much higher than that of Li2. This is why it is widely used in chemical vapor deposition as an inert gas, even though the nitrogen atom is highly reactive and readily incorporated into many substances.