Below I've got a circular needle inserted into the last row before the lace section and into the first row after the lace section.
I unpicked a complete row of the purple and unravelled it down to my knitting needle. I then carefully made sure I hadn't missed any stitches. I then did the same with the other lace section.
I now have two halves with all the stitches on a needle each. I needed to graft (kitchener stitch) the two pieces together and to do that, I unpicked the last row of the beige/pale pink yarn. If I'd grafted it as it is now, I would have ended up with an extra row.
After unpicking the last row of the beige/pale pink, I held the two pieces with right sides together and grafted the two halves together. I was working on the wrong side so it would look like a purl row on the right side as that's the row I'd taken out.
Here's the final result. I'm pretty happy with it. Once I've blocked it, it won't be obvious that I took out 20 rows of lace. I'm now working on finishing the last 20 rows and then I'll be blocking it. Hopefully it'll be dry so I can wear it when I leave for Bristol tomorrow.