Answer: Lindsey’s inventions are much safer than Edward’s.
In this sentence, the items that are being compared are Lindsey's inventions and Edward's inventions. However, as the second part is repetitive and it is easy to imply its purpose, the word "inventions" can be omitted. However, for the sentence to be clear, the possessive has to be maintained. Therefore, the correct way of writing the second party of the sentence would be "Edward's."