I think my question is purely theoretical and a matter of definitions; it derives from the fact that a L2-switch with VLAN capabilities is able to "create" different virtual LANs, and thus I am led to believe that "LAN" is a L2 concept. However, I've only recently thought about that, and I've always been used to the concept of LAN as a layer 3 thing, especially after university exercises. For example, if I have a network with a host, connected to a L2-switch, with the latter connecting another host and a router, then in an equivalent logical representation for identifying LANs, I would say that whatever is on one port of the router is a LAN, and whatever is on the other side is another LAN, thus replacing the switch with a "logical link". This makes me think, instead, that a router is what's needed to distinguish between a LAN and another - I can have multiple layer 2 switches and still be on the same LAN, provided that they don't use any VLAN capability. But then again, a router has both L3 and L2 capabilities, so this doesn't imply that a LAN isn't a L2 concept. I then thought, in order for 2 different LANs (or VLANs) to communicate, a router is needed, thus one may infer that when there's a router, it can be used to connect different LANs, hence we see it as a "LAN separator" in a logical scheme. But if that's true, then I can't understand what actually discriminates between a LAN and another, which factors do by definition. I may be confusing stuff, but I really can't find a precise definition for "LAN" as I only find very broad ones.
LAN is more commonly a reference to a layer-2 network but is sometimes used for a layer-3 network aka subnet as well. I don't think there's any "official" definition.
If you need to make the distinction you should use the layer names or numbers.
The term LAN is rather amorphous. It can mean a single broadcast domain, a network on a single cable plant, a network in a building or small group of close buildings, etc.
The context is everything, and it really depends on what you mean by "Local."