I am waiting for a possible job offer from an interview last week - I think I have a good chance of getting the job though there may be some negotiating needed around title etc.

My current employer wants me to schedule a business trip for the end of June... but I have to decide TOMORROW as it is being paid for by the vendor. I am getting a lot of pressure to go but how can I commit and then leave my job (if that's what happens)

Should I notify the HR person at the possible new company or make up a personal excuse as to why I can't go on the trip?

Be honest, it will look good on you. Notify the HR person at the possible new job. Don't jeopardize the job you already have.

You will only invent a tangled web of untruths you won't get out of!

Wait a minute... this is complicated by the fact that the business trip isn't until the end of June, and presumably the new job would start before then. But I too would call the new employer to ask how close they are to a decision, and I would definitely stall at your current job. They don't HAVE to have an answer right now. Make up something creative. A sibling's wedding is probably going to be that week or something, and you need a little more time.

I can't know enough about your current workplace or whether you interpreted the vibes from your interview correctly, or how much chance you really have for the new job--to be in a position to tell you to inform your current employer. That can be a career ender in many situations if you end up having to stay.
I think you need to deal with the facts as they are now, and let the chips fall where they may if you get the other job, unless you know your employer well enough to be relatively certain that they won't hold it against you.
You don't know what the future holds anymore than the rest of us do. Decisions need to be based on facts, not "I am waiting for a possible job offer from an interview last week ".
What's the worst that can happen if you set up the trip and don't go?