The OP was –
How do I handle new lots of raw materials in relation to the finished goods lot numbers?
As I understand the raw materials (solid/liquids?) are (somehow/somewhere/sometime) comingled. Without knowing some details it is difficult IMO to see how the OP can be answered in a very meaningful way. Hence i guess the appeal of gross descriptors such as time.
Just as an example I recall some previous threads involving silos continuously being topped up. From memory, on the “micro” level, it was necessary to visualize layers of raw materials moving through the container at the nominal flowrate but with a factor/assumptions to express the overlap of layers due mixing. On the “macro” level you simply had a time period where certain lots of inputted raw material were estimated to be “most likely” to be present in the output.
Clearly further variations in subsequent activities such as packaging will introduce ever more variables on top of the original varying stream.
Theoretically looks like a "typical" situation of (somehow) compounding mixing variances due to stages x1, x2, x3 etc. Practically, i suspect more likely a case of educated guesswork.
I anticipate that tagging exercises on incoming lots (Rfids?) have been done to evaluate the achievable accuracy of the OP's request ? It's clearly a fundamental Traceability problem.