Its weird though. That is never really mention again. Presumably Luthor is financing his later crimes and inventions from the money he stole from Warren Eckworth. But he was captured and sentenced to death for killing Eckworth. You would think that the authorities have learned of Luthor's theft of that money and froze his account.
Also in the alternate dimensions Lex still looks like Sherman Howard even though he would have never had reason to have plastic surgery.
My strained rationalization is that Eckworth was related to Lex Luthor. A later episode reveals that Lex killed his parents when he was growing up. BUT in a first season episode Lex mentions he has a wealthy father! Maybe Eckworth had an affair with Lex's mother. So there was a bit of resemblance between the two. Lex would have looked like a lot Eckworth as he aged naturally anyways. So with slight modifications, gaining weight, adding wrinkles he was able to briefly pull it off.