Transferring at Schipol airport

I recently went to Prague from Seattle. I went through passport control in Amsterdam, no security again. I already went through it in Seattle. I don't know about Lyon but I assume it should be the same as for Prague.

When I chat with AMS they say we have to do both. Has anyone gone
through this itinerary lately?

You chatted with AMS; what does that mean? You called the airport and spoke with which department or area at the airport?

I have flown through AMS on Delta and have connected on KLM to Vienna & Geneva just this year. As long as I stayed airside, there was no requirement to go through security.

I did the chat on AMS web site and first she said, I would go through passport control. So I answered, " so I won't need to go through security as well"? She replied, you will go through security too.
I usually get better luck just asking this group.

As far as I know, there is only security if the airport you came from does not have sufficiently rigid security. I think most US airports will have the same level of security, and therefore you should in principle not have to go through security again in AMS.

I did the chat on AMS web site and first she said, I would go through
passport control. So I answered, " so I won't need to go through
security as well"? She replied, you will go through security too. I
usually get better luck just asking this group.

Do you have a link? I'm curious as to where this chat agent can be found.

If you're arriving at AMS on Delta and are connecting to Lyon on KLM, you're not going to through security as you would if you were arriving at AMS by rail or street. That said, gate agents will check your passport and could remove you randomly from the jetway line to do a spot check and open all of your carry-on bags. That's happened to me on occasion at AMS.

https://www.schiphol.nl/en/checks-on-arrival/

There's a chance that you may have to clear Security and Passport
Control at Schiphol. This usually depends on where you are arriving
from.

If you are a transfer passenger from a country where the level of the
security does not meet EU-standards, you will have to pass through
central security.

https://insideflyer.nl/schiphol-central-security/

In the new situation there is a difference between ‘clean’ and ‘dirty’
flights. Passengers arriving from a country that has a screening level
that is approved by the EU (clean) will not have to go reclear
security when transferring. The screening on a Schengen-agreement
airport , EU country or US is deemed sufficient enough to pass
transfer without any further checks.

Transfer passengers

To separate passengers from cleared and non-cleared origin, new floors
have been built on top of the E, F and G piers.... If the aircraft is
arriving from a checked country (Schengen, EU or US) , then the
entrance to the Lounge will be used as is the case in the old
situation. Without any hassle passengers can shop and dine of go to
the airline lounges. If passengers are arriving in Schiphol they can
walk freely to passport control. Passengers who need to transit within
Schengen have only to pass the mandatory passport check between Lounge
1 and 2.

Since you are arriving from SEA (a US airport with adequate security), you should not need to be rescreened after passport control.

FYI, security procedures at Schiphol were revamped significantly in mid-2016, so some people may still be confused about how it works now. (You'd think anyone doing chat support on the AMS website would know by now - but ?). In fact, I did a connection from the US in 2016 similar to what you describe - and I had to go through security again after landing, but a few weeks later, Schiphol's security procedures were changed. What others are describing (no new security checks after landing from the US) sounds correct now.

In January 2017, transferred at Schipol going from Chicago to Venice. No security screening at Schipol for that transfer.

End of Sep 2017 we flew SEA to AMS, with connecting flight to Barcelona (BCN). That part was very smooth, not
having to go through security again. On the way back, our first leg was BCN to AMS. First, passport control,
then instead of being directed to the gate, we were directed to gate C1, where everyone who was flying to either
Seattle or Portland had to show passport and boarding pass, and was individually interviewed. This took a lot of time.
Then, we had to have our carry ons screened again, then we were individually told our gate numbers. At the gate had to show boarding pass and passport again. We had one hour between touch down and next flight and barely made it.
Unfortunately for two out of four of us, our checked baggage did not. We had gone through AMS just a year prior and
none of this was happening. The main message is to make sure you have enough time between connecting flights