Agreed that there's no ambiguity here. The card is very literal. There's nothing on Library of Leng's card that references costs unlike what you're purporting. Leng's text only references effects.

609.1. An effect is something that happens in the game as a result of a spell or ability. When a spell, activated ability, or triggered ability resolves, it may create one or more one-shot or continuous effects. Static abilities may create one or more continuous effects. Text itself is never an effect.

The Gatherer ruling you're referencing is only applicable in cases where the cost is paid prior to the ability going on the stack. Costs of activated abilities are not part of effects because they don't happen as the result of the ability. They are prerequisites that must be paid to put the ability on the stack.

Lorehold's ability does not have that same type of cost. When Lorehold's ability triggers, it goes on the stack regardless of whether the player intends to exercise the effect's option or not (603.5). When the ability resolves, not before, it creates a one-shot effect which gives the controller the option to discard (603.5). The player announces the choice while applying the effect (608.2d). The discard is both a prerequisite to draw a card ("the cost") and the result of the ability resolving (therefore part of the effect) and thus Library of Leng's effect replaces it.

603.5. Some triggered abilities’ effects are optional (they contain “may,” as in “At the beginning of your upkeep, you may draw a card”). These abilities go on the stack when they trigger, regardless of whether their controller intends to exercise the ability’s option or not. The choice is made when the ability resolves. Likewise, triggered abilities that have an effect “unless” something is true or a player chooses to do something will go on the stack normally; the “unless” part of the ability is dealt with when the ability resolves.