«لَا وَأَيَّدَكَ اللَّهُ»
No; and may Allah support you.
Here lā (لا) rejects an earlier assertion, while ayyadaka Allāh (أيّدك الله) invokes divine support for the addressee. Wāw helps signal that the negation belongs to the former proposition and is not meant to negate the prayer.
Without an adequate connection, a listener might incorrectly extend the denial to the supplicatory words. This is a specific function of waṣl for removing ambiguity (دفع الإيهام), distinct from simply putting two parallel factual reports together. The effect must be judged from the context, not from the particle in isolation.