Can you sue if someone affects your livelihood

And how exactly would one affect your livelihood? Did they cause irreparable damage to your business or business reputation causing a decline in your ability to make a living or get access to financial contracts? Or... something else?

The off-the-cuff answer is "sure" - because anyone can sue anybody for anything. But to give you a more specific answer, such as whether you have a viable cause for suing, we need to know what transpired. In what way did this person affect your livelihood? For example: if this person made false statements to your employer you may have a case. But if you have been stealing cash from the till and this person blew the whistle on you, then no.

As the others have noted its impossible to give you a reasonable answer based on such little information. Anyone can sue over anything. The question is whether you can win such a suit. The answer to that depends on the details of how you were wronged.

1) You work nights and sleep days. Your neighbor makes a lot of noise during the day. You fall asleep at work and get fired.
2) You say something nasty about your boss on Facebook. You get fired the next day.
3) A co-worker spreads rumors about you, and tells your supervisor that you shoplift. You do, but have never been caught, and the co-worker is the only one who knew. You get fired.

As stated above, you can sue anyone for anything. 1 and 2 won't get you a dime. 3 might.

Walmart opened a store in my home town. It caused business I worked for to close, and I lost my livelihood. But I can not sue Walmart. So, the details of the issue need to be discussed.