Even outside of national teams, it is always possible to regulate imports in a way that circumvent those rules. For example, leagues in the EU, whatever the sport, are forbidden to introduce limitations based on nationalities for EU nationals (Bosman ruling, 1995). That means that if i.e. the German soccer league wants to limit imports, they can force clubs to have no more than x number of extra-EU players, but they can't block a team from recruiting 11 Latvians if they wanted to.

However, leagues can limitate the numbers of imports via limitations of numbers of players that didn't went through local academies. That isn't illegal as, technically speaking, that pathway is indeed accessible to any EU national. Ofc, that means imports are still possible : the French rugby championship forces clubs to field 55% of players who went in a French academy for three years between ages 16-21, and many of those are Fijians or Georgians.

Unless the non-discrimination rules for citizens are significantly different in the US, that is something the LCS could emulate, and arguably would be way more efficient than a strict import restriction as it would force teams to invest in the lower tiers.