According to several trees on MyHeritage, there was another child born to this couple before Aaron in 1784.
William Pike was baptised 19th June 1779 in Amesbury, Wilstshire.
(I haven't checked this out).
I looked at several trees, but like you, no one seems to have found the marriage of Thomas and Rebecca Lawrence. Many have supposed it to be about 1778 in Amesbury.
If it's in the registers, you'd think somebody would have found it.
famiysearch.org have the films of Amesbury.
Unfortunately the BMDs are still only on film - not yet digitised, and the BTs are locked which means you can only see them at a familysearch library.
Rebecca was supposedly baptised March 18th 1762 at Milston. Father James, mother Elizabeth Hatherall.
If this is Thomas Pike's wife, she would only have been possibly just 16 years old if the marriage was in 1778.
Perhaps she was already pregnant.
Thomas Pike died 1834.
Have you looked for a will for him? You never know what might turn up in a will.
I'd also look at Rebecca Lawrence's family. Do you know when her father died? Have you looked for a will for him? Or indeed any other members of his family or the Pike family. Grandaddies, spinster aunts and bachelor uncles often left bequests to younger members of their wider family.
Just to add that people didn't always get married locally.
I have two people from Derbyshire in the very early 1700s, who I finally found got married in London.
It's definitely the same people - their parish in Derbyshire is written in the London register.
I still have no idea why they should have travelled 100s of miles to get married!
If Rebecca Lawrence was so young and already pregnant, they may have decided to travel some distance away from the eyes of local neighbours.
