Let's clear up some terminology first, sorry if I repeat some things that you already know:
- LER: This is a "Label Edge Router". These terminate MPLS LSP's.
- LSR: This is a "Label Switching Router". This is ANY router participating in MPLS.
- PE: This is a "Provider Edge". This is the device that is controlled by the service provider, closest to the customer equipment.
- P: This is a "Provider" router. Because PEs are at the edge of a network, you might have routers connect between PEs in a provider network, that's what P routers do (transit).
- CE: This is a "Customer Edge" router. This is the device that is controlled by the customer, these connect to PEs.
The more appropriate topology would look like this:
In this example, each device has the following roles in MPLS:
- CE1: This is just a customer edge. Typically, CE1 will use BGP to peer with PE1, though other options are available.
- PE1: This router is an LER as it is the ingress router (first router in the MPLS network) for the LSP that carries CE1's traffic into the service providers network. This is also an LSR, as it performs a role in MPLS.
- P: This router is an LSR, it participates in MPLS. This router is NOT an LER, as it does not TERMINATE an LSP.
- PE2: This router is also an LER as it is the egress router (last router in the MPLS LSP) for the LSP that carries traffic from CE1 to CE2 across the service providers network. This is also an LSR as it performs a role in MPLS.
- CE2: This is just a customer edge, just like CE1 it's probably going to be using BGP to peer with PE2.
You also had switches in the network, looking at your diagram it looks like your average switch, these will not participate directly in MPLS, and therefore are transparent to the network.
This barely scratches the surface, if you want to learn more about MPLS you can start reading this in addition to the other resources you listed.