Based on your comment in response to infinitezero's reply, I think there might be a translation-induced misunderstanding here. First of all, just to make sure we are on the same page, the lassen in the examples you bring up is part of AcI (accusativus cum infinitivo) constructions. In general, their structure is
AcI verb + accusative + infinitive. As you perhaps know, the class of AcI verbs in German is very small (< 10), with lassen by far the most commonly used (others are, for instance, heißen, machen, sehen). Simply put, in this construction, the
accusative does the action encoded in the
infinitive and the (finite)
AcI verb denotes a relationship between the sentence subject to that action. Eg:
Lass ihn gewinnen!
(= let him win). Here, ihn is the actant who wins and the addressee is instructed to allow for this action (ie, ihn's winning) to occur.
Crucially, however, your example
Lass dich nicht vom Bösen besiegen!
is not a prototypical example of an AcI. It is a very distinct feature of the AcI verb lassen, which, as far as I'm aware, is unparalleled in English (and, in fact, is limited to this one verb in German as well). Unlike in the canonical AcI, the meaning of the infinitive is essentially passive, not active, and the accusative complement is not the subject of the infinitive action but its object. The (non-essential) subject of the infinitive action is added in the form of a prepositional phrase with von or durch. So, in your example, the addressee is instructed to not allow for the evil to defeat dich, ie the addressee. Another example:
(1) Anna lässt Bernd [das Auto] reparieren.
(2) Anna lässt das Auto [von/durch Bernd] reparieren.
In both cases, Anna lets something happen, and in both cases, it's essentially the same thing. But in (1), reparieren has an active meaning and the subject of the infinitive action is Bernd. She lets Bernd repair. Das Auto can be added as an optional accusative complement to denote what is being repaired. In (2), reparieren has a passive meaning. Anna lets something happen, namely that the car is repaired. The optional prepositional phrase denotes the person who does the repairing. This analysis points to a slight semantic difference: In (1), the emphasis is on Bernd and the statement consequently has a permission/instruction-like undercurrent, while in (2), the emphasis is on the car getting repaired; there is less semantic value in lassen here.
The above-described passive lassen construction can be distinguished from an ordinary AcI by looking at the valence of the verb and relating the verb to the actants involved. Usually, there is no ambiguity. For instance, in your example, the prepositional phrase vom Bösen would make no sense unless the meaning is passive. Even if we ignore the (non-essential) von phrase, the meaning would be unambiguous, among other things because besiegen requires an accusative complement, so if you interpret dich as a regular AcI accusative (ie as the subject of the infinitive action), we would be missing an accusative complement. Conversely, in Lass uns ihn besiegen!, we would be looking at a regular AcI. The uns would make no sense in a passive construction because ihn would be the object of the infinitive action (the one being defeated) and, as you will recall, the subject would need to be added using a von/durch PP, so the uns would have no place here. (This paragraph probably sounds more difficult than the analysis is in practice. If you are aware of both AcI types in the case of lassen, it's usually intuitively apparent how it should be interpreted. Just think about the situation.)
Note: Your example (2), Er lässt mich bestrafen, is a rather rare case of ambiguity, potentially meaning both "He lets me be punished" and "He lets me punish". It is induced by the fact that bestrafen does not require a complement and that a non-essential accusative complement denotes the object of the bestrafen action. Within a neutral context, speakers would interpret it as "He lets me be punished", however. Bestrafen, as in English, is almost exclusively used with a [in German: an accusative] complement.