لِنُرِيَكَ (That We may show you) is in the subjunctive mood — it comes after a particle like أن ("that") or لن ("will not"), which changes its ending.

We translate it as "to [verb]" or "that [someone] [verb]".

لِنُرِيَكَ (That We may show you) uses form IV (أَفْعَلَ) — the أ at the start makes it causative ("to make someone do something").

We translate it as "to make [someone] do" or "to cause [action]".

لِنُرِيَكَ (That We may show you) starts with لِ showing purpose — it means "so that" or "in order to".

We add "so that" or "in order to" before the verb.