” Plug either lavalier into

" Plug either lavalier into the mixer channels 1 or 2, neither one makes sound. "             Is there a switch somewhere on your mixer which selects input levels ( mic / line )? Are the mixer input jacks " combo " jax; ie, XLR type with a 1/4" jack in the middle? Some gear uses these type input jax, XLR for mic level and 1/4" for line level.  The results you are describing sound likeng fed into a line level input.