Will my Dennie Morgan lines ever go away? (Photo)

You have some loose skin here.  Botox will not help with this, and Juvederm is not recommended for the lower lids.  You would benefit from some HA filler such as Restylane.  The additional volume will help to smooth out the whole area so you won't see the wrinkles.  Some laser resurfacing would also help to improve the texture.  A lower lid surgery to remove some skin may also help, but may need some filler post-op if still volume deficient.  

A combination approach will give the most improvement. Fillers, lasers, and microneedling/PRP can improve under the eyes. My patients try to get non surgical treatments to avoid surgery. We use PRP and stem cells there often. I suggest consulting with an expert to develop a treatment plan best suited for your short and long term goals. Best, Dr. Emer

Under eye wrinkles can be permanently corrected with surgery or temporarily camouflaged with fillers.There are great non-surgical options to fill in under eye depressions and hollowness. Using dermal fillers, a liquid eyelift can be performed. A dermal filler such as Restylane would be placed in the cheek and tear trough to hide the depression or bag underneath your eye.
Surgery would require a fat-repositioning lower lid blepharoplasty. In this surgical procedure, fat from the eye area is moved into the tear trough depression filling the actual depression. Cost will vary and can be discussed at your consultation.
I hope this helps!

It's difficult to assess the area fully due to your face not being at rest, but it appears you may have some loose skin and hollowness.  This is treated well with fillers to help disguise under eye irregularities.  Another non surgical option to consider is ALMI which uses your own tissues to add volume as well as improve skin tone and texture. 

Botox is not likely to help in this case. A skin tightening with a fractional CO2 laser would be my recommendation.