Personally, I don't think I understand the point of view to which the OP is a response. Rules and lore are both parts of the game to be enjoyed by its participants, but that is the extent of their similarity.
Lore relates to the setting of a particular session of roleplaying, and tells us what exists and what has happened.
Rules are the system by which the particular session is played, and tell us what happens as a result of play. Lore doesn't do that unless it has been codified into a rule.
There are various uses of "lore" and "rule". I think lore - as in
element of the shared fiction - can be, or give rise to, a rule - as in
a directive that governs the play of the game. But it doesn't have to. The converse is also true.
Lore equivalent to (or entailing) rules
For instance, it could easily be a rule that no dwarves may be wizards (by default, classic D&D has this rule). Is that "lore" or "rules"? Well, it's a directive with which game players are expected to comply - hence a rule. And it establishes some backstory - hence lore.
What about "that blue dragons come from the desert"? That seems like "lore". It can also be a rule, though - eg in some games it might govern the way the GM is allowed to frame encounters ("No blue dragon encounters in the middle of a swamp!").
On the other hand, that the dwarven kingdom to the north is called Forgehome (a solid, Dwarf-y name) seems like "lore" - as in, a piece of backstory local to this game at this table - but not a rule. (It doesn't really tell anyone about what they can do in PC building or encounter framing or action resolution.)
Rules equivalent to (or entailing) lore
Most players encounter the classic D&D restrictions on magic-user weaponry as a rule (daggers only! or daggers, staves and darts, but
definitely no swords!). But clearly it produces lore, in the sense of gameworlds in which wizards are never equipped with, or fight with, swords and maces. Hence the many discussions about how one might model Gandalf's use of Glamdring within a D&D framework.
Similarly, the fact that magic-users/wizards can't get healing magic like clerics can is normally first encountered as a rule; as part of learning the PC building rules and the spell lists associated with various classes. But it is also a major contributor to D&D lore - everyone knows that if someone is hurt you don't visit a wizard's guild, you go to a temple!
In worlds that use Rolemaster mechanics that same bit of lore doesn't get generated, because as well as clerical healing RM has a core Lay Healer class (analogous to a psionic healer in D&D, but the latter has always been optional, and most D&D worlds don't factor in psionic healing as a core component in world building).
On the other hand, here's a rule that probably doesn't entail some lore in any straightforward way: the old success-chance-by-level table for thieves. Another one might be the healing rules in 5e (some players interpret them as showing that, in the D&D world, recovery from injury is magically fast; some interpret them as showing that hp loss doesn't typically equate to significant physical harm; others just ignore or handwave the whole thing).
Gold for XP <snippage> and kingdom building were all rule things designed to enforce a certain game flavor.
These are examples where the rules don't quite
entail some particular lore - so they're not quite the same as the "wizards can't use swords or cast cure spells" rules in that respect - but the rules
tend to engender, through play, lore which has one sort of content and/or tone rather than another.
Other rules that I think fit into this general category are those that tell you whether it is hard or easy to take prisoners; whether monsters tend to attack or (as in classic D&D) have a reasonable chance of being friendly; whether evasion of pursuit is easy or hard; whether defeat of the PCs means TPK or being taken prisoner for ransom; etc.
Vincent Baker wrote
some interesting posts about this in relation to Lamentations of the Flame Princess: he was expecting one sort of thing out of the system (moralised horror) but the system (PC building, resolution mechanics, other stuff that he had trouble pinning down) pushed the game in a different sort of direction that he sums up as "Vance . . . [and] his ironic, cynical relativism".
Surely it's as simple as "the lore informs the role play" I.e. It provides context & richness to play off of.
One function of lore can be to "inform roleplay". But "inform roleplay" has different meanings.
Consider the suggestion on another thread that an ogre encounter might begin with the ogre throwing a half-eaten cow carcass at the PCs: the GM is using the lore to inform the set-up of the encounter. It's colour (or, if you prefer, flavour) that provides richness to the encounter set-up. But it probably doesn't inform the resolution of the encounter: eg nothing significant would change about the encounter if it was a half-eaten bear rather than a half-eaten cow; or even if the ogre through a log instead of a half-eaten carcass.
Another use for lore to "inform roleplay" - one that I myself prefer - is that the PCs are defined not just in mechanical terms, but in the relationship to certain elements of the shared fiction. So that the choice of how, in fictional terms, an encounter is set up by the GM doesn't make a difference just to "colour", but also to the sorts of goals the players choose for their PCs in relation to the encounter, and/or the way they actually engage the encounter via their PCs. A classic example of this is when (say) the ogre is really their dwarven friend who has been the victim of a polymorph spell. Now the players (in character as their PCs) have a reason not to want to kill the ogre, even if the ogre (with mind addled by the polymorph) is trying to kill them.
At least in my experience the more that a RPG group uses lore in this sort of way, the less the game has of "McGuffins", "sidequests", "fetch quests" and the like - stuff where the lore is colour but is not essential to the way the players engage the game and make their decisions - and the more it will be a sort-of dynamic back-and-forth between the players and the GM, as the players send signals about how/why the lore matters to them (and their PCs), and the GM uses that to inform the framing of the challenges that confront the PCs (and, thereby, the players).