At first I wanted to ask if Librem 5 supported eSIM but then realised that an eUICC chip is needed, so the answer is apparently no.
However, someone in the comments to this Reddit post claims that someone with Librem 5 has succeeded using esim.me (even though Purism is not in the list of their supported vendors).
Does someone here know anything about it? Is there any way of using eSIMs with Librem 5? Thanks 
I do use an esim.me SIM card in my Librem 5 (and I am the person who wrote that on reddit).
However, there’s no known way to provision such a SIM card with an eSIM profile on the Librem 5 (or any non-Android-running phone). Hence, I used my SHIFT 6mq to get the profile on the esim.me card, then took the card out and put it on my LIbrem 5.
there are actually free software implementations of the so-called LPA (local profile assistant) around. For example, the lpac program at GitHub - estkme-group/lpac: C-based eUICC LPA
The LPA is the connection between the eUICC chip and the SM-DP+ (server from which eSIM profile is downloaded).
lpac supports pcsc-lite to access smart card readers, so it should work right away when you use the smart card (not the SIM!) slot of a Librem5. For making it work in the SIM slot, the modem would have to support something like AT+CSIM (APDU tunneling over AT commands) and that would have to be glued as transport into lpac.
You might find Exploring eUICCs and eSIMS using pySim, lpac and osmo-smdpp - media.ccc.de interesting.
Note that using lpac or any other 3rd party LPA with esim me is a violation of their terms of service, so be careful about this specific product. However, there are other suppliers of eUICC In plastic card form-factor.
There is already an implementation of the AT interface have been tested with most Quectel LTE module (https://github.com/estkme-group/lpac/blob/main/interface/apdu/at.c), and a Linux GUI for lpac (GitHub - creamlike1024/EasyLPAC: lpac GUI Frontend).
I believe it is a good start point to implement eUICC on non-Android phone.