If lysa sends the vale knights when he receive robb’s missive, can they reach harrenhal before tywin ?

Well, there are earlier missives than Robb’s: Edmure sends a letter asking for help in Catelyn VII of AGOT, before the Lannister invasion of the Riverlands. Lysa’s refusal to help her brother, let alone Robb, is what gets Brynden Tully to quit as the Knight of the Bloody Gate.

So yeah, it’s possible.