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I am planning to travel to the US under the VWP (I am a Spanish citizen). I will be visiting a university lab, but I am not receiving any salary or income from them and they will not benefit from me being there, so it should be ok according to B-visa purposes (and thus VWP):
Reference document from travel.state.gov, see "Researcher" on page 2.
What documents should I bring with me to show to the border officer?

This is just an answer from my own experience rather than an authoritative written source.

Back when I was a PhD student, I did this several times a year. I was a British citizen attached to a U.K. institution informally invited to assist in work at a couple of US laboratories. By "informally invited", I mean, the US lab would ask my advisor to assist them, but he didn't want to go so he would ask me to go instead. This would be arranged by emails and usually I would get notice of it a few days beforehand from my advisor, if he remembered to tell me. I was not paid by the labs but I sometimes received travel expenses from them. I always entered under the VWP and was (as now) often questioned about my purpose. On no occasion was I denied entry, sent to a secondary inspection, asked for any documentary evidence, or the like.

Essentially, the conversation would go like this---and usually they only asked the first question before jumping to the end.

Me: Good evening, how are you?

Friendly CBP man: "What is the purpose of your visit?"

Me: Business.

CBP: "What kind of business?"

Me: Scientific collaboration.

CBP: "What kind of science?"

Me: I'm visiting Lawrence Livermore National Labs for three weeks to assist in a science experiment.

CBP: stamp

[I believe it is best to avoid the word "work" in these conversations. You are not working for the US lab, so don't say "work". If you say "work" then the CBP officer may have to investigate exactly what you mean by "work".]

This was in common with other members of my UK-based group; the only chap who had trouble entering the US from time to time was because some CBP staff enjoyed asking lengthy questions about why he had the name "Mohammed". But even he wasn't denied entry.

Once I had a CBP officer who was surprisingly knowledgeable about Debye shielding in plasma physics, and who seemed to want to catch me out in my explanation of how to derive it (a harder question than I ever got in my viva!), but that was it.

Of course your experience may be different, but in my recollection I am not aware of any researcher holding a European passport who ever encountered difficulty in entering the US under these circumstances.

You definitely should get a letter of invitation from the institution stating the duration and motive of your stay, as well as the fact that you will receive no compensation for what your're doing.

This is a sample letter

This is because when a VWP national presents their passport, they apply for admission in WT (tourist) status by default. You, however, want to get in in WB (business) status, which has slightly more privileges (explained below); hence you'll want to convince the CBP that that's the status you should be admitted in.

On its website, the University of California states, regarding visiting them for lab observations/research:

It is not appropriate for WTs to participate in UCSF activities.

In essence, doing activities that could be considered a form of work (but of course without being paid by a US employer) is not recommended if in WT Status - therefore if planning to do them, one should enter in WB status, and double-check the assigned admission class written by hand below the entry stamp.

If using an APC kiosk (which you likely will - depends on the airport), select WB as the desired admission class.

What documments should I bring with me to show to the border officer?

Theoretically nothing. This is not a visa interview. But you are being prudent which is never a bad idea.

I will be visiting a university lab, but I am not receiving any salary or income from them and they will not benefit from me being there

This. Exactly this. I presume this is a longer, arranged visit so get a letter stating this from the university lab on official letterhead and stamp. If it contains the name and phone of someone the CBP can contact it's even better but I sincerely doubt you'd need that on the border.