Is it permissible to lie if it harms no one and offers a personal benefit for travel, and would the earnings acquired after this travel be unlawful?

The default is that lying is forbidden, condemned, and prohibited, except in specific exceptional cases. Lying to circumvent a country's entry requirements is not one of these cases. The Prophet (peace and blessings be upon him) said: «Indeed, truthfulness leads to righteousness, and righteousness leads to Paradise. A man continues to be truthful until he is recorded as a Siddeeq (truthful one) with Allah. And indeed, lying leads to wickedness, and wickedness leads to the Fire. A man continues to lie until he is recorded as a liar with Allah». And «Deceit and treachery are in the Fire».

As for someone who entered by means of forbidden lying and then performed a permissible job, their work is not forbidden to them, unless the employer stipulated that the worker's entry must be lawful.