The statement " If L1 and L2 are non regular languages then L1 U L2 is also non regular" is false.
Because,
Let L1={ aⁿbⁿ | n>=0 } which is non regular language (L1 is a deterministic context free language)
L2 = complement of L1 , which is also a non regular language. L2 is also deterministic context free language as dcfl is closed under complement operation.
Here L1 U L2 = ∑*, which is regular language.
But if L2 is not the complement language of L1 then L1 U L2 will not be regular language.