I would think you would need, as a first step, to find an expert in textiles of the period to examine the lace and ensure it is not made of materials (fibres, dyes) or using techniques that were invented after Marie Louise's life. If you were really determined (and had the money to burn) you could also have a sample tested using Chromatography or other techniques that can help identify the age of the object.
All of this will, of course, only tell you if it is even possible that Marie Louise could have owned the piece. You will still have to prove that she did own it.
Establishing provenance, or the unbroken 'chain of custody' of an artifact can be difficult even if the piece is something notable (jewellery, furniture, etc.) that has been described in leters, wills, estate inventories, memoirs, and bills of sale. A single piece of lace would be infinitely harder (not impossible, but very close to it)
You should start by writing down everything you know or have been told about the lace and how it came to be in your possession. For example, maybe the piece of lace has been handed down from your X-Great Grandmother who received it from her sister-in-law who was a seamstress to Marie Louise. Now you have to prove the entire story with research - the aforementioned letters, wills, memoirs, bills of sale. If it is a unique design and if it was, say, depicted in a painting of Marie Louise that can also help but you will still need to prove the entire story.
To reiterate this will likely not be easy by any measure. If you choose to try, all I can say is good luck.
