When joining manufactured welting or cord-on-lip, I have always left the ends loose & then tried to twist, contort, glue, tape, etc. the ends together. The other day I was making pillows & realized that if I SEWED the beginning end down in the position where I wanted it to end up after being joined, that I had less work! So to begin, simply rotate the cord-on-lip apart (you don't have to take the lip off) & sew across the strands that you want to keep.
Sew welt around your pillow until you get to the joining spot. With your fingers (again you don't need to take off the lip) just unroll the strands of the cord-on-lip.
After you have tested to see that the join is even, just sew over the strands in that perfect position.