Step 1: Analyzing lithium compounds.
Lithium is a small cation with high charge density and can react with nitrogen to form lithium nitride (Li\(_3\)N).
Step 2: Analyzing Be(OH)\(_2\).
Be(OH)\(_2\) is amphoteric, not purely basic, so option 1 is incorrect.
Step 3: Lattice energy consideration.
LiF has higher lattice energy than LiCl because fluoride ion is smaller than chloride, making option 2 incorrect.
Step 4: Superoxide of potassium.
Potassium superoxide (KO\(_2\)) is paramagnetic due to the unpaired electron in the O\(_2^-\) ion, so option 4 is incorrect.
Step 5: Conclusion.
Thus, the correct statement is option 3: Lithium can form nitride with nitrogen.