Can Botox help marionette lines and a vertical forehead line that are not caused by movement? (photos)

Forehead lines are most frequently caused by certain facial expressions, which is why they respond best to a neuromodulator like Botox. Botox relaxes the muscle that forms the line, reducing the wrinkle in the process. The treatment can even help the creases that have become permanently etched in the skin over time. Your case is mild and I suspect after one or two sessions of Botox, that line will disappear! In deeper lines, the addition of small amounts of dermal filler can further enhance the result. However, there are risks associated with using filler in the forehead area, so make sure the doctor you work with is both board certified and highly experienced in this procedure. 
Lines around the mouth typically form when collagen levels in the dermal structure decline. As collagen is depleted, the skin becomes lax and creases can form. Dermal fillers work very well in these areas, restoring the support needed to smooth away the wrinkles. This treatment also requires precision and expertise to produce the best possible result. A qualified doctor should be able to help you achieve an excellent result for both of your concerns. 

Thank you for your question. Botox is a neuromodulator that targets facial muscles responsible for some types of wrinkles. As the medication relaxes the muscle, lines due to facial expressions like smiling and squinting are visibly reduced. This is the common reason for lines in the upper face, including the vertical line you see on your forehead. Over time, these lines can become permanently etched into the skin, so they are visible all the time. 
Lines that form around the mouth are more frequently caused by collagen loss, which occurs naturally as we age. Collagen is a vital protein that supports the dermal structure, and lower levels over time can lead to skin laxity and wrinkle formation. These lines are most effectively addressed using dermal fillers that restore volume to the dermal layers to smooth away wrinkles. 
I encourage you to schedule a consultation with a board-certified dermatologist who is also an expert in these injectable treatments. Through a careful assessment and discussion of your concerns, your doctor can recommend the best treatment plan for you. 

The marionette lines are often improved with filler.  If the lines on your forehead are static (not caused from muscle activity) then Botox would not improve them.  A great place to begin is a consultation with an experienced injector to discuss your concerns and learn about your options.