In my initial answer, I just tried to put myself in the OP's boots, pretended to accept the way his dependency grammar and its derived parser seemed to work (to the extent that could be inferred from the parses he offered), and simply argued in favour of the parse that violated FEWER of the most obvious empirical adequacy constraints that any credible grammar of German should comply with. So, (omitting references to notational obscurities I initially pointed out concerning the interpretation of 'OA','OC' and the reason for the '1', '2', '3' numbering that have since been clarified) I wrote:
"I am no expert in dependency-grammar-based parsing, but, anyway, since beeindrucken is an obligatorily transitive verb, unless there is a direct object-on-verb dependency between the reflexive sich and beeindrucken, the rules of German grammar would be violated. As, on the other hand, lassen, in its 'causative' interpretation [Addition: a crucial qualification!], selects an infinitive (i.e., it does not select sich at all), the only parse compatible with the axioms of dependency grammars (or those I am familiar with, anyway) and with the constraints imposed by German grammar is one that reflects 1) a direct-object-on-verb dependency between sich and beeindrucken, and 2) a complement-on-verb dependency between beeindrucken and the verb lassen, but no direct dependency at all between sich and lassen. In other words, your first parse above is not correct and the parser is 'right' to offer the second parse as the correct analysis (obviously, under dependency-theory assumptions...)."[Emphasis added: again, a crucial qualification, as explained below]
That was a silly mistake, and it serves me right that my answer should have been downvoted. What I should have done instead is a) insist on the obvious idea that hopelessly superficial, incomplete, and blatantly ad hoc grammars can never support serious parsers or yield adequate analyses of anything but the most trivial sentences; b) plainly say that neither of the parses offered above can remotely capture the syntactic and semantic complexities of the sich beeindrucken lassen construction; and c) explain why. Since my earlier answer may have confused readers, let me do so now.
The problem with the first parse is at least twofold. First, that, although, in other uses ('main verb' ones), lassen can, indeed, be 'monotransitive' (e.g., Lass die dummen Witze!), 'ditransitive' (cf. Ich lasse mir Zeit), or, indeed, even 'complex transitive' (cf. Lass ihn weiterschlafen) or 'transitive' with an obligatory adverbial PP (e.g., Er lässt uns nicht in die Wohnung), the fact is that 'modal (and, semantically,'causative') lassen, like all German (non-elliptical) modals, must select an infinitival clause (as in ...einen Arzt kommen lassen): it cannot select any NP argument because it has no theta-role to assign to it.
The second, and tougher, problem is that, whereas when the infinitive (clause) is active, as in the latter example with kommen, its accusative subject (einen Arzt) suffices to satisfy the argument structure of kommen (a 1-place predicate) - and the same applies to 2-place infinitives like untersuchen in ...einen Arzt das Kind untersuchen lassen, whose two arguments are satisfactorily discharged by the two accusative NPs, etc. - in cases like the OP's ...beeindrucken lassen, the infinitive is not active, but passive, in interpretation, and, of course, even its reduced argument structure remains unsatisfied (and the infinitive itself uninterpretable) if it has no dependents at all and its 'passiveness' is left unexpressed, as proposed in the 1st parse above.
Given such circumstances, the parser designer would minimally have to 1) posit an entirely ad hoc additional lexical entry, a passive verb beeindrucken (apart from the, independently necessary, active 2-place verb beeindrucken), and 2) offer explicit rules/principles determining how passive beeindrucken behaves syntactically and semantically, but, of course, nothing remotely like that is shown or can be inferred from the first parse above.
As to the parser's own parse, the second one, at first blush (and always taking dependency grammar for granted!) it seems somewhat less inadequate than the first to the extent that it, at least, captures the structural dependency between the infinitive beeindrucken and its modal governor lassen, but it is still hopelessly incomplete and superficial to express the syntactic and semantic structures that make ... sich... beeindrucken lassen behave as it does and mean what it means.
In this case, the problem is threefold: a) beeindrucken is still incorrectly treated as if it were 'active' and 'transitive' (i.e., 2-place), and it is, accordingly, granted by the parser a direct object (= sich) which is supposed to satisfy its internal argument (the Theme, Experiencer, Affected, ... whatever the thematic role label is in the parser's internal grammar), but b) it is not additionally provided with any NP dependent that may satisfy its 'higher' argument (the 'beeindrucker': an Agent, Cause(r), Stimulus,... whatever the semantic role label is in the parser's underlying grammar), which violates indispensable and nowadays cross-theoretically accepted syntactic-semantic principles (e.g., depending on the theory chosen, Functional Saturation, Satisfaction, The Theta Criterion,...) and leaves the infinitive clause with an open variable and no well-formed semantic interpretation. Finally, c), the 2nd parse raises a further problem that the 1st one did not cause: reflexive sich being an anaphor, it must be 'bound' inside its 'binding domain' (= the infinitival clause sich beeindrucken, here), but, of course, it is not, since that clause has no internal subject (say, a hidden PRO-like one, assuming beeindrucken were active, which, as stated, it is not) and the nearest antecedent and potential binder can only be outside (an argument of the superordinate clause), which means that, under the second parse, 'sich' is referentially uninterpretable. That leaves us with two serious flaws even in the parser's own parse.
In sum, as soon as the dependency theory framework underlying the OP's parser is itself questioned for its flagrant inability to reach minimal standards of descriptive adequacy, an issue I wrongly avoided to go into in my earlier answer, the 2nd parse is actually more problematic than the first. Adequately parsing German (or Spanish, French, etc.) apparently active infinitives with passive interpretations (just as parsing English apparently active gerunds with passive interpretations) requires much more powerful and sophisticated grammars than the one underlying the OP's dependency-based parser above.