"I will treat him to lunch."

So in England "invite" is not quite the same as "treat" in that I could "invite" a number of people to gather at a restaurant for a meal but it doesn't necessarily mean I will pay for them all - we may end up splitting the bill for example. If someone uses the word bjuda is it unambiguous that they are saying they will pay ? If so, is there a word in Swedish that mean "join me for lunch/let's go have lunch together" which everyone understands that it means they may have to pay for themselves ?

Is this a correct sentence: 'Jag ska bjuda honom lunch' - If it was translated as 'I will offer him a lunch (as an exchange for his breakfast). Whereas 'bjuda på' would be 'I invite you to lunch with me and I will pay for your lunch'.

Why not "I am going to ..." That is a plan and nothing I do not have any influence on...