How to create a money tournament?

I've seen some tournaments where you can win money. Is anyone allowed to start these tournaments whenever they want?

As long as it's your money, I can't perceive a reason why not.

Gotcha. Whats the process to get one started?

That I cannot answer, pal.

I never set up a tourney on my own, but hopefully someone with more knowledge on the subject will catch a glimpse of your thread ... how did you plan to transfer the money to the winner anyways (just curious)?

Just go to play, tournament, set up a new tournament, choose the time control and the duration and the starting time and the conditions for entry. Give it a suitable name e.g. 5+3 money tournament 18h00 - 20h00 GMT.
You can also post a message on this discussion board stating the time control, time, duration, the amount of money you donate and the price distribution: 1st price ....$, 2nd price ....$, 3rd price ....$ and the condition for entry.
You can pay the prices as bitcoins, but also through Western Union or SWIFT bank transfer.
I do not know how lichess intended to pay out prices for their money tournaments, but the winner Magnus Carlsen twice donated his price money back to lichess.
Be sure to wait for cheating check before paying out the price.
A first price of €1000 seems sufficient to attract the elite of the world.

See lichess.org/blog/WjgXRCcAAOMX_1VF/lichess-titled-arena-2 and lichess.org/tournament/WfvjOFkB for inspiration.

@Teho120 Good question, but I can not answer. Maybe you need to contact the administrator saying you want to sponsor a tournament. lichess.org/contact

Lichess should consider setting up a way for people to donate to a prize fund. Even if people only put in a dollar or two we'd build up a decent fund pretty quickly.