Correct spelling for the English word "letted happen" is [lˈɛtɪd hˈapən], [lˈɛtɪd hˈapən], [l_ˈɛ_t_ɪ_d h_ˈa_p_ə_n] (IPA phonetic alphabet).
The phrase "letted happen" does not have a distinct etymology as it is not a commonly used or recognized phrase. However, breaking it down, "let" is an English word derived from Old English "lǣtan" meaning "to allow" or "permit". In this context, "happen" refers to an event or occurrence. Together, "let happen" would mean to allow or permit something to occur.