The correct answer is A. It encapsulates IP packets from non-LISP sites with a LISP header.
In Cisco LISP, a PITR (Proxy Ingress Tunnel Router) provides connectivity between non-LISP sites and LISP sites. Cisco documentation states that a PITR performs ITR mapping database lookups and LISP encapsulation functions on behalf of non-LISP-capable sites. Cisco also explains that the PITR attracts traffic from non-LISP sites that is destined for LISP EID space, then encapsulates and forwards that traffic to LISP sites.
That is exactly what option A describes.
A PITR acts like an ingress tunnel router for non-LISP sources. When traffic comes from a non-LISP site toward a LISP destination, the PITR:
receives the traffic,
performs the mapping lookup,
adds the LISP header,
and forwards the encapsulated packet toward the correct LISP site.
B. It accepts registration requests and aggregates successfully registered EID prefixes to client ITRs. This describes the role of a Map Server (MS), not a PITR. Cisco states that the MS receives registrations from ETRs and advertises aggregates for registered EID prefixes into the mapping system.
C. It is responsible for publishing the site EID-to-RLOC mappings. This is also associated with the Map Server / mapping system, not the PITR. The PITR uses mappings for encapsulation; it does not publish them.
D. It forwards encapsulated messages to the MS to the authoritative ITR for the EID. This is incorrect terminology and mismatched function. Cisco explains that a Map Resolver (MR) accepts encapsulated Map-Request messages from ITRs and forwards them toward the appropriate Map Server or authoritative ETR, not an authoritative ITR.
ENCOR exam point:
Remember these LISP roles clearly:
ITR = encapsulates traffic toward LISP sites
ETR = decapsulates traffic arriving at LISP sites
PITR = performs ITR function for non-LISP to LISP traffic
MS/MR = mapping-system control-plane components