Definition of Gi-LAN

As you probably know, UMTS/GPRS and LTE/EPC define a series of "reference points", which are points of logical interconnect between component systems, with "interfaces" defining the signaling and bearer data delivery mechanisms between the connected components. The SGi reference point describes the point of logical interconnect between an EPC network and a different packet data network (PDN), while the Gi reference point describes the point of logical interconnect between a GPRS network and another PDN.

"S/Gi LAN" is not, to my knowledge, defined anywhere in the 3GPP specifications, but can be understood as the IP network infrastructure immediately on the PDN side of the S/Gi interface. It would, then, be (as you say) the "implied network interconnected to the Gi/SGi interface".