Where does “Lamerik” come from?

Lamerik (Mauritian Creole) comes from French Amérique, from New Latin America, from Italian Amerigo, from Proto-Germanic *Amalarīks, from Proto-Germanic Haimarīks, from Proto-Germanic rīks, from Proto-Celtic rīxs, from Proto-Indo-European h₃rḗǵs — to straighten, to right oneself; right; just.

Ancestry of “Lamerik”, step by step

StepLanguageWordMeaning
1FrenchAmérique—
2New LatinAmerica—
3ItalianAmerigo—
4Proto-Germanic*Amalarīks—
5Proto-GermanicHaimarīksHenry
6Proto-Germanicrīksking, ruler
7Proto-Celticrīxsking
8Proto-Indo-Europeanh₃rḗǵsking, ruler
9Proto-Indo-Europeanh₃reǵ-to straighten, to right oneself; right; just
Every word from Proto-Indo-European h₃reǵ- →Every word from Proto-Indo-European h₃rḗǵs →Every word from Proto-Celtic rīxs →