2005 Buick La Crosse engine losing oil

ya it does, check for a intake manifold problem either cracked/broken or the seals are bad an d sucking oil into motor.

But if oil was being sucked into the engine through the manifold wouldn't that oil burn and cause smoke and smell?

Could the oil be leaking into the coolant system?

oil could be doing either you may not notice it if it were burning if slowly have your coolant system pressure checked for an internal leak

if slowly then I would agree but as I wrote we lost a quart in 10 miles of driving. That aint slowly.

that is why I said it' may be an intake problem and sucking it in you'll have to remove it to see.there is a tsb on exhaust valve seals and using oil there . one thing you have to remember aif it is using oil like you say then a lot will get used up in converter and won't smoke because of how hot the converter runs. So pulling the intake and looking is first step. Also Gm recommends to let engine sit off for 15 minutes prior to checking oil as it may be to full. also make sure dipstick is fully seated into block.