Schubele has good points. There is also another option, which is of lower data quality, but is still usable when the flow in question is of low relative importance in the LCIA.
If you know the input material, and the production process, you can model the production of the product yourself. You will not know if this is 100% correct without having secondary data to support transport, waste %, and specific energy consumption in production, but you can get close enough that i t wont matter.
That is how i would approach this, from a practical standpoint.