My fading memory tells me this:
1. The lot number will only tell you what plant/company manufactured the item. LC is Lake City, TW is Twin Cities (long since closed) , TZ is somewhere in Israel, etc. All you're going to see on 5.56 or 7.62 is the manufacturer code and date, never a lot number.
2. The second two digits of the NSN are a country code, and I "think" it means the country that designed the item. Small arms begin with 1305, and the 00 or 01 that follow indicate a US-designed item. An 02 or above is another country.
3. Larger rounds such as 20 or 30mm could have the entire lot number painted on the case or the cartridge, but probably not stamped into the headstamp.
4. The best source of info on a particular lot is the ammo data card (ADC), which is the "birth certificate" for the lot. That will tell you where and when it was made as well as lot numbers of components (primer, powder, etc). However, end users are not likely to see the ADC, only the ammo storage people (461s in the AF, 55X in the Army).
Disclaimer: I said it was a FADING memory.