How can I secure vinyl plank flooring that has lifted?
Ans OP question in comment.  
Updated to change the glue to be used. 
1. to help with the glue mess, place transparent packaging tape along both edges.  Tape as close to the edge as possible.
2. You may have to insert a couple of thin wedges, screwdriver, etc. in the gap to get enough clearance to get the glue in
3. use a glue wedge tip or screwdriver to push the glue in the gap and underneath the plank


I would use Gorilla Glue Clear, which is waterproof and glue most surfaces.  This is only a small area. 
After inserting the glue into the gap, wipe off any excess.
lay a layer of wax paper over the repair area.  this is to prevent the glue from sticking to the heavy weights that you will place on top of the gap to push it down even to the floor.
Place heavy weights on the gap and wait for the glue to dry.


If your scotch tape can hold it down, then this should work.  See what comments are posted on the use of Gorilla Glue Clear as the glue for this solutions.
Caution:  Make sure it is Gorilla Glue Clear,  other Gorilla products may be the forming type, which you do NOT want to use.