About 6 months ago I bought 10 metres of a very light weight DuPont Lycra to make myself some new summer underwear but when it arrived, instead of being on a roll, it had been folded and crushed into a postage bag and when I got it out it was this incredible crumpled mess. I wasted about 1 metre of it playing with it and trying to work out how to handle it but it was so light that it would stretch just picking it up and handling it. I put it aside until I had a bit more time to work on it. Some months down the track I came up with a number of pieces of genius along with a lot of trial and error until I got it under control.
The reason for the requirement is I wear stubbies for most of the hot weather so I don't get cooked in the heat but you have to be careful what you wear under them as conventional men's briefs drag the behind up when you sit or squat. A thong of the right design does the job properly in maintaining normal modesty while not cutting you in half and staying up. A thong pattern for lack of better words is a simple thing to make but only if you can work out how to handle such a difficult fabric.
Step 1. Cut strips wide enough and lay them one at a time on your cutting table, a few weights helps to keep it flat. I used an iron with a teflon bottom cover to carefully iron it flat without cooking it, turning it over a couple of times to try and stop the edges from curling.
Step 2. Use some masking tape across the top and bottom of the strip to secure the edges and make the fabric so it can be handled and stop the top and bottom edges from curling.

I could not get the camera up high enough but you can see the strip of lycra clamped with plastic clamps at both ends off the edge of my cutting table. The next operation is almost impossible to photograph but it uses 2 strips of rubber edging that have glue from a craft glue pen on one side then carefully turn the rubber strip over, stretch it very slightly and press it down onto the edge of the fabric allowing a little overhang on the outside edge for the following overlocking of the rubber onto the fabric.

Overlock the rubber edging onto the edge of each side of the fabric, it should look something like the photo. In this case I used a 4 thread overlock but it comes too close to the inside edge of the rubber and while it works OK if you are careful, pulling out one needle in the overlocker to get a narrower overlock would work better.

Turn the overlocked rubber over then face stitch it from the front with a medium width zig zag.

This photo shows the technique for marking out the profile required using a template rather than a conventional pattern. Clamp the top and bottom of each side (one at a time) along the edge of the table making sure you only barely stretch it. Then lay the template on the fabric, line it all up straight and clamp the template into position. Then you very carefully chalk around the template profile without applying much pressure as normal chalking drags the fabric. You hold down the edge of the template as close as possible to the edge to make the chalking easier.

This is what the chalked profile should look like after you remove the clamps and template.

I used some miniature paper clips to hold the two outer edges together after folding the vertical strip length ways and lining up the two edges. I have tried pinning, basting is a waste of time in a fabric like this and it has been the most effective method and the easiest to use.

The next operation of making the main seam is a bit fussy. To match the stretch rate of the fabric I tested out a wide variety of techniques to get a stitching method that had enough stretch and the best I found was one of the cams for my old Elna's that does a sideways zig zag back and forth as this allows a stretch rate very close to the lycra. I am sorry if the stitching is a bit faint but I used a small automatic camera that was not well geard for this task.

This shows the item after it has been trimmed. The two ends have been cut off and the stitching like from the template markout has been trimmed to about 1.5 millimeters from the edge of the stitching. I tried a range of different stitches to stitch down the seam but the best of them still ruined the stretch rate of the seam so I decided to leave it unedged as the fabric is a stable knit and does not fray.

This is the finished garment from the front. The center zig zag line onto the elastic was done first after using the miniature paper clips to locate the front part of the strip to the elastic. The bottom line was done next so that the zig zag went over the bottom edge of the elastic then to top edge was trimmed to get it level with the top of the elastic and it was zig zagged so that the stitching went over and secured the edge on the elastic.

The back is attached the same way, the red top stitching was for sighting the long center seam so I could see it after the stitching and as a garment of this type is not normally on display while wearing it, I could not be bothered changing the thread colour.