I am having Juvederm injected into my lips Monday evening. Will biking 6 hours, at a moderate pace, on Tuesday affect my lips?

Follow your injector's instructions. If you have substantial swelling and bruising, it's better to wait until it goes a way a bit before exercising.

It is recommended that you wait a few days after your lip filler before exercising. Juvederm draws water after injections so that with the combination of exercise can make it worse for you. 

Each injector has his or her guidelines for post treatment care. You may wish to delay the ride for a day or a few days (if possible). Consult with your injector as he or she knows the scope of the treatment and the specifics about you.

There are no good studies that look at exercising after filler injections but I usually advise people to minimize activities that will significantly raise their blood pressure as that can contribute to swelling.  Juvederm absorbs water during the first 48 hours and so often there is an "over-correction" or very full appearance to the lips at first which is normal and goes away.  It is unlikely to significantly alter your final result but I'd discuss that with your injector.  What I do warn patients about is not to manipulate the area for the first 48 hours with intense kissing, massage, etc so as not to misdirect the filler and have them use ice compresses while in the office for 10 minutes immediately after injection.  If you do plan to take the trip, you can ask your doctor about a low dose of oral Prednisone after treatment because that might help a bit with swelling that you may get.I hope that helps!

If you are going on a bike ride like you are describing, it is probably best to wait until after the biking to make sure you maximize the results from the procedure. You can always find someone willing to do the injections, but these products can swell, and with exertion this swelling can get even worse. Wait; you will be much happier in the end.

Lip augmentation certainly can be performed, but you will be swollen before going hiking, and you might even swell more while hiking too.

Performing rigorous physical activity post injections to the lips, may cause more swelling then you would otherwise have after treatment.   

The lips tend to swell after fillers, and Juvederm tends to have more intense swelling than other fillers. Also, a lot of times people don't realize the lip biting or intense faces they make during exercise, so even though the biking itself won't cause an issue, other factors around it may not be the best for your newly injected lips.... at least for a few days!"This answer has been solicited without seeing this patient and
cannot be held as true medical advice, but only opinion. Seek in-person
treatment with a trained medical professional for appropriate care."

The Juvederm will cause swelling, and exercise can make it worse.  Over the days after injection the Juvederm actually attracts more water into the tissues. Putting off your bike riding for a week or so might be a good idea. Also, I am sure your injecting physician has his/her own recommendations for post injection treatment.  Talk to him or her.