I have found this website that claims that to get visa upon landing in Bangkok I will need passport and return ticket.
My passport is European (Lithuanian) so this one is covered, however I am planning on flying one way (as I will be staying for some time in each of SE countries) and already have bought the tickets.
How strongly is the requirement to have return tickets being enforced? How big of a risk am I running of not being able to enter the Thailand?
People from most countries don't want a VOA, they just want a visa waiver, which will allow them into the country for 30 days. Citizens of Andorra, Bhutan, Bulgaria, China, Taiwan, Cyprus, Ethiopia, India, Kazakhstan, Latvia, Maldives, Malta, Mauritius, Romania, San Marino, Saudi Arabia, Ukraine, Uzbekistan, and, like the OP, Lithuania will have to go the more cumbersome VOA process.
The actual Thai immigration authorities are very lax on the onward-ticket rule for visa-waiver. In fact, they are completely lax. In 16 years of traveling to Southeast Asia, I have never heard of a citizen of a Western country being asked at the Thai border to produce proof of onward travel.
Your problem is not the Thai authorities, it's the airline. If a passenger gets somewhere and that country won't admit him, it's the airline's problem to get him home. Plus, if this happens often enough, the airline can be fined, or even ejected from the country!
The fact that the Thai immigration people are very lax won't help you if the check-in clerk doesn't know that. The clerk does not want to get her employer, and derivatively herself, in hot water.
Most countries, so many tourists go to Thailand that the clerks are completely aware of the lax Thai policy. Most countries, but not all: I have heard several complaints from New Zealand and one each from Japan and the Netherlands.
So, if you're at all worried, here's what you do:
The whole thing will cost you about $15 and 30 minutes, but it's extremely unlikely to happen.
Edit: Pnuts points out that the OP is Litvak, and so not eligible for a waiver. Yes, he would need a VOA. I have no idea how strict they are, so the FlyOnward option becomes all the more attractive.
OP, after you do this (presumably with a real or virtual onward ticket), please report back.
Further Edit: the VOA is goddamn 2000 baht, that's $57 or €52.50. That's a lot of money. You might look into the cost of the real visa from the consulate in Vilnius.
Still Further Edit: Checked in for a NokAir flight in HCMC yesterday bound for DMK and the counter agent wanted the boarding number for my onward flight. NokAir is Thai-owned so they definitely know how un-enforced the rule is -- and in fact, the immigration agent when I landed did not inquire -- but it may be company policy.
The first hurdle will be the airline you are flying to Thailand with. They are required to make sure that you have the documents required to enter the Kingdom. One of the required documents for a VOA is an air ticket departing within 15 days. So in practice, the check in agent should not allow you to check in or board without it.
If by chance they are extremely lax, then Immigration will want to see your air ticket before they issue you the VOA. They may also want to see proof of financial means which is determined as 10,000 baht (or equivalent) in cash (25,000 for a family). Major credit cards may be acceptable, depends on the officer checking your application.
The risk you encounter by not having a return or onward ticket: loss of non-refundable airfares, hotel bookings, etc if the airline refuses to board you; being sent home on the next plane if Immigration stops you (plus loss of non-refundable bookings as above).
