If I understand you correctly, these are two separate questions.
In Isa 53:6, you are asking whether "him" can refer to God (יהוהhere יהוה) rather than the implicit subject of verse 2–5 (thus affirming the identity of the faithful servant and God, which is what you want if you explain this as a prophecy about Jesus). Yes, this is possible. As in many languages, referents are often ambiguous.
While there is no dedicated word for 'himself', certain nouns can be used to highlight such reflexivity, e.g. בנפשׁו 'on his soul/spirit/...' or בראשׁו 'on his head'. But this is entirely optional, and when it is not included this cannot be taken as a hint that a reflexive meaning is not intended.
In Gen 22:8, you are asking whether the preposition ל can mark the direct object (a second direct object next to 'the lamb') of the verb. This is not a question of referent identification but about the function of the preposition and its use with this verb. No, I do not think this suggestion can be upheld. While the so-called lamed obiecti (i.e., using ל for the direct object) is common in some strands of Aramaic, and entered later Biblical Hebrew as well, it is not typically used in old texts as these (the normal object marker in Biblical Hebrew is את). Furthermore, verbs with double direct objects are rather rare, and such a construction is as far as I know not attested for this verb.
Alternatively, you may consider 'the lamb' to be in apposition to לו ("God will provide him, i.e., the lamb, ..."), but in this case you would expect the preposition to be repeated: לו להשׂה instead of לו השׂה.
Seeing that the normal reading ("God will provide the lamb for himself [i.e., God]") makes perfect sense there is also no reason to move to more dubious grammatical interpretations.