The Swedish Empire would be smothered - Gustavus was a leading, inspirational and almost divine figure in his own right and is still considered the most powerful, influential and all-round greatest Swede, for turning Sweden into a leading power that stood against the juggernaut of Catholicism.
Although with a weakened Sweden, I wonder what would happen with European politics. England and France were on the rise during this time, and Russia was trying to expand its power but its westward expansionist aims were strongly curbed by Sweden's near-hegemony on the Baltic and Eastern Europe after the Great War's peace was secured. While I think that the Anglo-Swedish alliance would still persist and a new rivalry with France would ensue like in our history, it would be much weaker and wouldn't necessarily force France to renege on its agreements in favour of courting Spain and the Italian states.
Russia as an even greater power than at present, however, is rather less within the realm of possibility. Still, assuming events following a hypothetical death of Gustavus at Lützen go really badly for Sweden and leave it weakened and disunited, it would present Russia with the best opportunity to fill the void in such a case. But again, it assumes things do not go Sweden's way at all.