I'm not sure if this is of any help, but I found this on the 1871 IoM census.

Name: Andrew Linchey
Age in 1871: 50
Estimated Birth Year: abt 1821
Relation: Head
Spouses's Name: Jane
Gender: Male
Where born: Ireland

Civil parish: [Douglas]
Town: Douglas
County/Island: Isle of Man
Country: Isle of Man

Street address: View image
Condition as to marriage: View image
Occupation: View image
Disability: View image

Registration district: Isle Of Man
Sub-registration district: F
ED, institution, or vessel: 16
Neighboors: View others on page
Household schedule number: 181
Household Members: Name Age
Andrew Linchey 50
Andrew Linchey 11
Charles Linchey 8
James Linchey 23
Jane Linchey 50
Jane Linchey 13
Mary Linchey 19
Robert Linchey 4

It states his occupation as a rag and rope merchant.

On the 1851 he's a labourer, and the name is spelt as Lynch.
Andrew Lynch
Age: 30
Estimated Birth Year: abt 1821
Where born: Ireland
Relation: Head
Spouses's Name: Jane
Gender: Male

Civil Parish or Township: Conchan
Town: Douglas
County/Island: Isle of Man
Country: Isle of Man

Street address: View image
Condition as to marriage: View image
Occupation: View image
Disability: View image

Registration district: Isle of Man
Sub-registration district: Not Stated
ED, institution, or vessel: 7
Neighbors: View others on page
Household schedule number: 61
Household Members: Name Age
Andrew Lynch 30
James Lynch 4
Jane Lynch 30
Sarah Lynch 9

I can't find him on the 1841.

I found on the LDS IGI

Search Results | Download | Pedigree

--------------------------------------------------------------------------------

ANDREW LINCHEY
Male Family

--------------------------------------------------------------------------------
Event(s):
Birth:
Christening:
Death:
Burial:

--------------------------------------------------------------------------------
Marriages:
Spouse: JANE IRVING Family
Marriage: 15 JUN 1841 Ballaugh, Isle Of Man, England

Sorry I couldn't have been much more help. It's very difficult to find out about Irish descendants.