You asked about this earlier - I suggested that you use the newspapers to determine if any court appearance as I don't think any of the various court documents of this period have been digitised
some mention of Public companies can be found under B240 on my subject index page - links to 1889 + 1894 companies are there (the Manx Museum has info on dissolved companies to abt 1911 after which you need approach general registry).
I've only researched up to 1847 when land registration scheme changed and also later in 19th Cent company law went through many changes following changes in English law - however assuming it is Andrew Lynchey you are researching I doubt if he would be registered and thus only trading as a sole trader - certainly prior to 1850 this would mean he would be sued for debt probably in High Bailiff's court and if debt proved and he could not pay the coroner(of his deputy the Lockman) would be entitled to seize property and put it for sale by public auction - in all the pre 1847 deeds of such sales the document would give the date of the court decree authorising sale - catch is that the deed is indexed as under Coroner's name and not that of the original owner - hence difficult to find unless either you know the buyer and approx date of any sale

I suspect you will have to employ a local researcher as such searches are extremely tedious (I've seen some land conveyancers spend expensive days in Manx museum)