Long story short, it's not worth it at all. I'll take CS:GO as an example since that's the only game I have experience with playing competitively:
You would need at least 3000-4000 hours, have a team of similar skill that you also gel well with and you would need to win online tournaments against the top 24 teams in the country to qualify for LAN.
Once you get to play in a major LAN (which there aren't many of in SA even for CS:GO which is the biggest game in the country), you would need to come in the top half of the teams competing to even earn a single cent in most cases.
Pretty much all the LANs are hosted in JHB, so if you don't live there you would need to provide your own transport and accommodation unless your team is getting that sponsored (which is very unlikely since there's simply not enough money involved for companies to be interested).
So what's going to land up happening even if you qualify for LAN is that you land up spending more money going to the tournament than what you get from it, unless you are one of the top 4 teams in the country.
In first world countries where players get paid a salary, it might be somewhat worth it. But here there's simply not enough money or interest for you to get anywhere. I would rather look at something more long term like streaming if you want to make actual money.