U2417H, daisy chain to monitor HDMI?

That would not work because the LG 29UM59 is using 3rd party DP to HDMI cable to HDMI in port. The entire daisy chain has to be DP or mDP. See the online U2417H User's Guide page 28.

HP Elitebook DP out port --> U2417H DP to mDP cable --> U2417H mDP in port (Menu-Display-MST On)
U2417H DP out port --> DP to DP cable --> Second monitor DP in port

-or-

HP Elitebook DP out port --> U2417H DP to mDP cable --> U2417H mDP in port (Menu-Display-MST On)
U2417H DP out port --> DP to mDP cable --> Second monitor mDP in port

@Rinze  and @DELL-Chris M , this actually might be possible with a slight modification.  It is true that DisplayPort daisy chaining requires native DisplayPort along the entire chain, but there is a bit of a workaround that you should be able to apply for the last display in the chain that would allow the last display to use HDMI.  It involves an active DisplayPort to HDMI adapter like this one.  Whereas the vastly more common passive DP to HDMI adapters/cables rely on the DisplayPort source supporting "Dual Mode DisplayPort" and falling back to HDMI signaling, which isn't allowed on a daisy chain, this active adapter accepts a native DisplayPort signal and converts it to HDMI within a chip built into the adapter.  As a result, the daisy chain THINKS that DisplayPort is being used throughout the entire chain, and since you'd only be doing this on the LAST display in the chain, it shouldn't matter that you're giving that display an HDMI signal.  I say "shouldn't" because I have not personally tested this, but I believe it would work based on my understanding of the underlying technologies.  But this would definitely NOT work anywhere "upstream" in the chain because a display receiving a signal on HDMI can't pass a daisy chain signal farther down the chain.

But if you want to give it a try, please report back as to whether it works!

Thanks for your quick reply Chris! 

What's your take on @jphughan statement? 

Dell has never tested/validated the usage of DP MST with a DP to HDMI active converter. Could it work, unknown? For $17, to me it is worth trying.

Thank you for your quick response!

Maybe this is a rookie's question, but could it in any way damage my laptop or monitors by trying this?

Also, is there any other way to find out if an adapter is active? For example, would this also classify as active: 

https://store.hp.com/NetherlandsStore/Merch/Product.aspx?id=F3W43AA&opt=&sel=ACC

@Rinze  You definitely won't damage anything.  Worst case you won't get an image on the display connected through the adapter.  As for identifying whether an adapter is active, typically it will explicitly state that.  Another common indicator is mentioning support for AMD EyeFinity, since those setups do not allow Dual Mode DisplayPort, which is partly what made active DP to HDMI adapters more popular.  Unfortunately I don't speak Dutch, so I can't comment on the adapter you found.  But active adapters are much more rare than passive adapters overall.  Additionally, you have to be careful about the DIRECTION of the active conversion, because there are ALSO active HDMI to DP adapters that are designed to convert an HDMI source signal to a DisplayPort output, which is the opposite of what you are trying to do.  So even when you're researching adapters that are known to be active, you have to be careful about what you're buying -- although those types of active adapters would not mention EyeFinity support since that direction is not useful for EyeFinity.

But if you're in the Netherlands, then I found that same Plugable adapter I mentioned on the Amazon Netherlands store here, although it does seem to be quite a bit more expensive.

Thanks for getting back to me again!

I noticed the big price difference too, which is why I started looking for alternatives. I'll see if I can find something more in the previous price range and let you know whether or not it worked.