England, easy, almost did. Right persuasive person at right time and place persuades right person. I think it might not even require any change to the 39 Articles. I'm assuming here that "Lutheran" is used in a confessional sense. So we are saying a Church of England that looks to the Confession of Augsburg, rather than the Heidelberg Confessional . England would probably want to retain bishops and the traditional church polity (that's OK, there have been Lutheran bishops, or 'supervisors' , same word).
One point though, might that upset the marriage of the Princess Royal to the Elector Palatine? James was dubious about it as was, the religion being the same (both Calvinist, Palatine explicitly so, CoE implicitly) made a difference. If that is butterflied away you butterfly away the Hanoverian succession.
Scotland, bit harder, but the same deal.
Ireland. Almost ASB unless in includes a greatly more widespread Cromwellian settlement. The problem is that at the important 16th century period, the England only controlled a very small part of Ireland, and the rest was extremely backward, splintered and reactionary. Very hard to evangalise. Also, Ireland would tend to want to do whatever England didn't.
Still, maybe if Elizabeth was a Lutheran (she would have been OK with that), and her conquest attempts in Ireland went off better. At least, an Anglo-Irish Ascendancy which was Lutheran Church of Ireland (Same as Church of England) instead of OTL Calvinist-Anglo-Catholic-BitofEverything. )