Warning: opinionated ranting follows; some people claim to love the side lugs.
The design stinks, IMHO. Leica recognized this when they changed M5 spec to 3 lugs.
The best answer is to add a strap lug on the right side. Sherry uses a genuine Leica M5 replacement lug, for something under $150 IIRC. Other repair pros should be able to do something similar. DIY at your own risk.
Unmodified, even a plain neckstrap doesn't work well, since the back and body need to be separated to load film, and each strap end attaches to each piece. The body is heavier than the back, so if the camera is hanging around your neck and you don't hold both halves, the body wants to crash to the ground when the back is removed. Oops.
Luigi cases are things of beauty, but with a CL you need four hands to hold the three pieces (body, case and back) and load film. Case cost similar to right lug retrofit.
Gordy straps are great, but the tripod mount strap needs to be removed to load a CL (can't remove the back with tripod socket occupied). If you use the thumbscrew model, the camera profile is 1/2" higher, no longer as compact. If you use a bolt model, you need a tool/coin to remove the strap---inconvenient. A tripod-mount neckstrap would have the camera hanging upside-down, which I don't even want to think about. So you're limited to a wristrap here.
A single-lug Gordy strap, either thread-mount or o-ring, can be attached to the body lug. The body hangs funny/crooked and the back is unattached when removed, but at least the body will safely hang from your neck (or wrist) when loading film. The o-ring would cause considerable paint wear on the body lug.
My favorite cheap solution so far is to connect the two lugs with a nylon/web strap, then attach a single-lug Gordy o-ring neckstrap to the half of the lug strap that attaches to the body (hard to describe, so photos attached). The body strap is just long enough to allow the back/body to separate, and the single-point neckstrap mount keeps the body and back hanging together, even when they're separated. When the back is attached, the camera weight is supported relatively evenly by both lugs, so the camera hangs straight and doesn't sway like it does when the neckstrap is attached directly only to the body lug.
Next time my CL needs a CLA I'll have a right-side lug added. I think I'd still leave the back tethered to the left-side body lug, so it can't get dropped.
YMMV.....