All well and good for t1, but then I need a new utility function for the next moment, t2, and places infinite weight on lying at t2 but not at t1.
Why at t2 must you no longer place infinite weight against lying at t1? It would seem that if you did not, in fact, lie at t1 (and you can infallibly achieve this) then leaving the infinite dis-utility for lying at t1 makes no practical difference. Sure, if you ever tell a single lie all subsequent behavior will become arbitrary but that possibility has been assumed away.
Provided you have infinite confidence in the impossibility of time travel or timeless decision theory style entanglement of past events with your choices now, that's right. It's not as problematic as placing infinite weight on lying at t2 when it's still t1 (which would license lying now to avoid future lying, contra deontology).
This was demonstrated, in a certain limited way, in Peterson (2009). See also Lowry & Peterson (2011).
The Peterson result provides an "asymmetry argument" in favor of consequentialism:
Another argument in favor of consequentialism has to do with the causes of different types of moral judgments: see Are Deontological Moral Judgments Rationalizations?
Update: see Carl's criticism.