You need the verb "contar" in this sentence because you say "contar uma mentira" for "to tell a lie". You also use "contar" in "contar uma história (to tell/narrate a story)", but you can't say "dizer uma história".

I try to think of 'contar' as 'to recount'. As in, 'to recount a story'. This helps me remember when to use 'contar' or 'dizer'.