Hello Adam!
Firstly, John Mueller from Google said that HTML lang attribute is ignored as a ranking factor.
Here some articles:
Google: We Ignore The HTML lang Attribute - The SERoundTable
Why Google Ignores HTML Lang Attribute for Indexing in Search Results - The SEMpost
You should use Hreflang,
Here some really useful resources about that:
Multi-regional and multilingual sites - Google Search Console
International checklist - Moz Blog
Using the correct hreglang tag - Moz Blog
Guide to international website expansion - Moz Blog
Tool for checking hreflang anotations - Moz Blog
Secondly, yes. It could help creating a separate page for differente audiences. Remember to create a completely original and different page for both countries. And of course use correctly the internationalization tags.
Hope it helps.
Best Luck.
GR