@hikermor is right--if you're prepared, then the trip can still be enjoyed. But if you aren't prepared, or more importantly if you aren't willing to endure the conditions, you might want to change your plans.
I'd highly recommend calling the San Isabel/Pike Forest Ranger office to see if they can offer you better advice or direction as they'll have a clear idea as to what the weather will be like in the Lost Creek area.
At any rate, you can always ditch the backpacking plan and go car camping instead to ensure you'll have a hard shelter, but you'll probably have to settle for dispersed sites as reserved sites will likely be full over the Memorial Day weekend.
It looks like many areas in Colorado are going to experience a typical early-summer weather pattern this weekend--afternoon thunderstorms following clear mornings--but on Monday in Bailey it's supposed to rain consistently and be unseasonably cold.
If you need another last-minute idea, it looks like the weather isn't supposed to be too bad in the Steamboat Springs area--there are some neat backpacking options near Rabbit Ears Pass and on the east side of Routt County in the Medicine Bow-Routt National Forest. Steamboat is 4-4.5 hours drive from Denver International Airport.
Hope this helps!