If I look at the center of Amsterdam, in the past year there have been losts of tourists from all over Europe even when bars and restaurants are closed. So this means that any strict lock down would have to be coordinated at least within the EU.

In the past, EU countries did not want to delegate health care to the EU (except for approving medicine). So this would require lots of individual countries (including Sweden and, until this year, the UK) to suddenly agree on a single strict lockdown. Very unlikely to happen.