You could say it is an adjunct of space / a locative adjunct, more specifically one that indicates direction: it is then used metaphorically, as lead is also used metaphorically—the case is not leading a person or cattle to some physical place, but it is metaphorically leading events along a causal chain towards a result, or something like that.
As an alternative, you could say it is an adjunct of consequence/result, or something like that, if you treat the metaphor as a starting point for analysis. Frankly I don't think it matters a great deal how you classify adjuncts, as long as you classify them as either adverbial or attributive/adjectival, i.e. determine whether they modify a verb or something else.
It could also be argued that the directional to phrase with the verb lead is a complement to the verb instead of an adjunct, if one considers a constituent/argument/phrase of direction indispensable for this verb. That is, you could argue that lead requires either an object, a direction, or both to make sense (elliptical use notwithstanding). A verb can have several different uses/frames with different meanings, each requiring different kinds of arguments/constituents. A subject is nearly always required.
She led him to the volcano. (Both
object and direction required for the
sentence to make sense.)
Who will lead us? (Only an object is
This path leads nowhere. (Only a
direction is required.)
The white ship leads! (Nothing
required—except the subject.)