Although he's poor, he would never stoop to lying.

Literal

Poor [although-だけれども] he [topic-は] lie [object-を] tell [such-ような] thing [topic-は] does-not-do.

けれども is the most formal variant of the けど/けれど family. ようなことはしない means 'would not do something like that' — ような connects lying to the type of behavior being denied. The は in ことは adds emphasis to the negation, drawing a line.