"modern research says it is not Lugh's festival but instead 'the festival at which law judgements are given'."

This research is suffering from myopia! It's looking at a painting through a magnifying glass. It's seeing one tiny detail in great detail but has utterly lost sight of the bigger picture. The key questions are:

1. why is the word "law" so similar to the names "lugh" and "llew llaw"?

2. why are judges called m'lud?

It should be remembered that Odin was a divine judge, daily "giving judgement" at the foot of Yggdrasil.

In short, I'd say it was both Lugh's festival and 'the festival at which law judgements were given' - the two are not at all mutually exclusive and it's not an either/or situation.