Here is what I found worked for my "new to me" Nikkor 3.5cm f2.5 LTM lens. Still no luck with filters, but at B&H I found this front lens cap, which fits nicely:
https://www.bhphotovideo.com/c/product/157529-REG/Schneider_91_030245_36mm_Push_On_Lens_Cap.html
And this rear M39 threaded lens cap:
https://www.bhphotovideo.com/c/product/1419099-REG/fotodiox_cap_rear_m39_slvr_premium_metal_rear_lens.html**
**Just a word of caution on the rear lens cap, B&H and Fotodiox did some kind of weird thing and some of the Fotodiox M39 items are not what is pictured on the B&H site. This was a real issue with the M39 body caps they make, the design is totally different (and doesn't work on a Barnack) from what the web site shows. The rear cap I currently have was a bought a couple years ago, and it's perfect. Just make sure you keep the receipt until you get the item and make sure it fits and does what you need.
Hope this is helpful. I'm happy to now have a front and rear cap for this little lens.
Best,
-Tim