Was Robb lying to Edmure?

[Chris Mormont]

Robb didn't lie, but he was also in the wrong.

If Robb wanted Edmure to allow Tywin to follow him, then Robb should have been clearer with his orders.  When Cat is told "Ser Edmure is protecting Robb's rear, that could be an assumption made by the man and Ed.

While it may have been Robb's intent to stretch Tywin out and cut his supply lines off, the rest of his "plan" finding a place to ambush tywin would have been a hope not a definitive plan.  As for keeping him away from Kingslanding, that was all based on 20/20 hindsight.  No one thought Stannis would defeat Renly's army, and most believed that the 2 brothers would have a large battle before either of them turned towards KL, at which point the victor would need to regroup and deal with the casualties.