what to expect at AMS: time needed and passport control

A step at a time. There is no passport control in AMS for the train. You go through security and immigrations in London prior to boarding the Eurostar. It can be a bit of a zoo getting through in London so I would go at least an hour early if not more like 90 minutes. Lines can be very long but move fairly quick.

Is the flight from AMS to Frankfurt a connecting flight to LAX? If so, you should then be at AMS around the two hour mark since it is just a domestic flight. It is a little unclear. Is she spending time in Amsterdam prior to continuing to Frankfurt. In Frankfurt she will go through exit immigrations and security.

Thanks. I try to be more clear. She is spending 3 nights in Amsterdam and then the flight home starts at AMS,
she changes planes at Frankfurt and flies on to LAX.

I've never flown out of AMS but everywhere else I've been in Europe when flying back to the US you go through customs and security at the international point of departure. The issue then becomes having enough time between landing there and the scheduled departure. After a dozen flights into Finland and back, I had a 100% record of missing the connection when going through Stockholm and connecting on to Oulu because of tight connections not allowing enough time to get through customs. After the first time I knew the drill and could relax knowing I'd eventually get there. Coming back out of Europe to the US always seems to take longer than you would expect and if your flight from AMS to Frankfurt doesn't have at least an hour or so before departure they might want to think about an earlier flight from AMS.

I can recall one time we were flying back from Frankfurt and barely made our flight even arriving almost 2 hours before the departure because of terminal changes and construction.

Bottom line, I'd rather be waiting in the departure lounge enjoying a cup of coffee and light meal than wondering how I'm going to get home after missing an international flight.

We flew AMS->FRA>-PHL last month, with less than 95 minutes (IIRC) as scheduled layover. We had no issues whatsoever, with a lot of time to kill, even with our incoming flight not gating but busing. The extra step of security going up to the "Z" level for US flights took about 1 minute extra to go through. same last year when we similarly flew this return but from Copenhagen. One thing we did note, we were hungry, having left before breakfast, and there was very little to choose from after going through security to Z deck. If you need something, grab sandwiches or such on the way to Z deck before you get up there (or in Schiphol), there will be a lot more to choose from. As long as these are both Lufthansa flights the transit between the two gates should be straightforward and not particularly far.