This is not the aqua blue sleeve, but is the same pattern shape.
The sleeves and linings are sewn up and then I stab-stitch the seams open.
You can see the tiny dots running along the outside of the seam below.
Once the seams are finished, I put the 'good' sides of the sleeve and lining together (so that I can see the messy inner seam on my side) and run a line of stitching around the top of the sleeve to join them together. If there are tabs on the top of the sleeve, you need to position them before you sew this seam, and also make sure that they are positioned so that they won't move around when sewing (and crucially) so that the tabs will be on the outside of the sleeve when you turn it the right way out.
Once this seam is sewn, I put clips in the seam allowance to reduce puckering when the sleeve is turned the right way out.
Next, I turn the sleeve right way out. All seams should be hidden inside the sleeve and only nice finished seams visible when you look inside as well as on the outside. I usually put a line of small whip stitching around the top of the sleeve to make sure the lining doesn't roll out or move.
Notice the whip stitching around the top of the sleeve.
Making sure that the lining is not tucked up inside and is sitting smoothly, I measure my hem allowance. I also zigzag my edges for durability.
This sleeve has been hemmed; you can just see the tiny dots showing on the outside which is the hemming line. I clip triangles into the outer and inner fabrics to reduce puckering and bunching.
I prefer to hem my lining separately to reduce puckering. I use a little whip stitch, same as on the fashion layer of fabric.
Working the eyelets on top of the sleeves: the holes correspond with the ties in the gown. I make a hole with an awl, and then increase the size of the hole with a bigger awl that I made out of a wooden knitting needle. I go around the hole with a line of double running stitch. I usually use four strands of thread for strength. I don't use buttonhole stitch because I think it adds too much bulk on top of the double running stitch - I just go over the edges with satin stitch. The eyelets turn out very durable and are big enough that lucet cords can be threaded through without needing a bodkin. This is important as friends usually lace my sleeves on for me at events and I don't want to make it harder for them than it has to be!