Learn Turkish: Adam bana yalan söylüyor gibi geldi. - It seemed to me like the man was lying.

The verb gelmek (to come) is used with gibi (like) and a dative pronoun, which is bana (to me) in this sentence. Literally, the structure translates as "It came to me like...", which is the standard Turkish way to express a subjective sensory impression or say "It seemed to me that..."

Why is söylüyor in the present continuous tense when the main verb geldi is in the past?

The phrase before gibi acts like a snapshot of your thought at that exact moment. When you were observing the man, your thought was, "He is lying" (yalan söylüyor). Therefore, you use the present continuous tense for that inner thought, even though the realization itself happened in the past (geldi).

Could I use a complex noun clause here, like Adamın yalan söylediği gibi geldi?

No, and that is what makes this structure so convenient! Unlike verbs that require a complex noun clause with possessive endings (for example, Yalan söylediğini biliyorum - I know that he is lying), the gibi gelmek structure simply takes a full, regular sentence right before gibi. You just state adam yalan söylüyor and attach the rest.

Why is bana placed after Adam instead of at the beginning of the sentence?