Realistically, the League of Nations was probably doomed as soon as Wilson proposed it. It sounds nice on paper, but ok, assume that "works" = "works as well as the UN". The UN did not prevent major powers from starting wars with minor powers. The UN does stop some minor wars between minor powers, and provides a forum for big powers to work on issues (Cuban missile Crisis). So things to change.
1) Security council made up of all major powers, so say need USA, UK, France, Germany, Russia, Italy, and Japan as permanent members to work. Also better if no one power has a Veto. The problem is that German, USSR, Italy, and Japan will all undermine the council due to war grievances. So one by one.
2) Germany: Has to be a soft peace that is seen as fair by the Germans. So, German keeps 1914 borders, adds Sudetenland and Austria in exchange for League of Nations membership and light reparations to Belgium only. Pure ASB. But if this does not happen, one of the most powerful countries in the world will be undermining the League. Or some similar "fair" ToV.
2A) Or, Just occupy German for two generations like USA and Soviets do in OTL after ww2. So Britain and France each have to agree to keep 500K troops in Germany for 50 years. Also ASB.
3) Western power immediately accept communist rise to power and recognize Lenin in November 1917. Entente also accepts Russia withdrawal from the war, and no Japanese, British or American troops on Russian soil.
3A) War ends in 1916, before the Tsar is doomed.
4) Italy - Britain/France can't backstab Italy, Italy must get the Balkan land it was promised and at least one new colonial possession. This is quite doable, except it embarrasses Wilson, so war needs again to end in 1916. Wilson needs to not issue his 14 points.
5) Japan needs to have clear limits it can live with. This is doable if Japan is treated as equal to white powers. So ASB.
6) Britain would need to maintain a standing army of 1 million men and 2 million reserves. Britain would also need to be willing to use this army to enforce League Mandates.
7) Then to be credible, the security council would have to work out the details of the post WW1 peace. Even if in early 1916, each sides armies declare a cease fire but stay in place and the blockade is lifted, there are many details that are hard to work through. Poland, Belgium, German Colonies, reparations, if/how to resume trade, the Armenian issue, etc.
The UN works to a large extend due to American Naval and Logistical power. The League failed because Britain and to a lesser extent France were unwilling to pay the cost of the standing army and navy required. Britain and France were also unwilling to do the soft peace of WW2. The USA helped rebuild German and Japan, Britain and France wanted reparations from the Kaiser. The goodwill effect of British merchant ships unloading food in German ports a few days after the cease fire would be hard to overstate. People remember who feeds them in famines, even generations later.
I would say the only realistic way would be for the "league of nations" lead by Wilson to actually negotiate a soft peace to WW1, no later than Mid-1916. This league that settle the war now has prestige, and can be finalized by post war treaties. This is also ASB.