Honestly, I dont understand what is lottery you are talking about. Maybe this is football finals feature, but in ice hockey, you just go online and buy ticket. Or buy tickets from resellers at the stadium. Right now you can freely go to
https://www.lippu.fi/en/artist/2023-jaakiekon-mm-kisat/2023-jaeaekiekon-mm-kisat-3218460/?pnum=2 and buy a ticket for gold medal game. 150 EUR and you will see which ice hockey team is the best in 2023.
Lets take Frankfurt, Germany airport (one of the biggest and busiest airports in Europe) as a centre. Google say that cheapest one way airplane ticket is about 400 EUR. Same google say that Tampa hostels starting price is 40 EUR, taking into consideration, this is IIHF finals, everything will be booked, so I would double the price.
Total: 1000 EUR to see IIHF World Cup final + the amount you spend to get to Frankfurt + beer
The problems you might get - all the cheap tokens for prelims are already sold out now, but if you are alone and dont need 5-10 seats in a row, you still can get a ticket with a little effort.
P.S. Prelim tickets were starting from 12.50 EUR for a weak teams games, or from 22 EUR for games such as Canada vs Finland during prelims (but such tickets were sold out immediately). If you are from Europe, a bus from most of countries to Tampa would cost 20-50 EUR max, take some junk food with you and it will cost around 100 EUR to watch your favourite team play. 100 EUR can afford to spend most of average fans.
When there are important games in soccer, often times more people want to see the game than there is capacity in the stadium. That is when they accept applications for tickets until a deadline and then they run a lottery in order to determine who is going to get a ticket and who is not- I have no idea about ice hockey and whether it is so popular that more people want to see it than there are tickets to be sold.
I am mot sure whether lotteries are run for the World Cup, but if I remember correctly I think it has been like that in the past. Perhaps only for the final and semifinals, but I don't know.
When you are alone it is of course much easier to organize such a trip to the World Cup, but i believe that usually people would travel there at least with two persons or in small groups. It does need quite a bit of planning in advance.