My father believed that anyone who can't make a living in Japan is lazy.
Literal
Father [topic-は], Japan [at-で] livelihood [object-を] make-continue-cannot person [topic-は] lazy-person [copula-だ] [quotative-と] was-believing.
生計を立てていけない uses three layers: 生計を立てる (make a living) + ていく (continue into the future) + ない (negative) = 'can't sustain a livelihood.' 怠け者 ('lazy person') ends with 者 (もの), a common suffix for types of people. The whole thought is embedded as a belief with と信じていた.