Yes, it is safe to carry the LC9 with the safety off and a chambered round. My Kel-Tec PF9, similar in size and weight, also has a double-action trigger mechanism, and has no safety.
It takes a deliberate, firm, rearward pull of the trigger to set off a double-action firearm from a "hammer-at-rest" (or "striker-at-rest") mode.
It is safe to carry the P-64 with the safety off as well (assuming the hammer is "at rest".)
My PF9 is currently loaded with basic Remington-UMC 115-grain JHP ammunition. This ammunition functions well in my gun, and has been (historically, at least!) readily both available and affordable locally. I feel that I would get some enhanced ballistic performance with a 124-grain load, which I think is about what my gun is sighted for (it shoots low with lighter ammo.) However, I have not run across any that is affordable and available enough for me to proof its function (typically, I require a hundred rounds to proof. If I have a failure, I require a hundred rounds of flawless function beyond that failure.)