There is a great deal of information missing from your query, although it is likely that you have little information. For example, do you have any idea when and where Henry Piers was born?

You mention locations, 'Fulham' and 'Lincoln', but Lincoln, for example, could be any of numerous Lincoln's including Lincolnshire, England, Lincoln, Nebraska a multitude of Lincoln Counties or Lincoln Co., Ontario.

Two Henry Piers are mentioned in the Social Security Death index:

Henry PIERS
Birth Date: 14 Jan 1901
Death Date: Feb 1969
Social Security Number: 118-14-6755
State or Territory Where Number Was Issued: New York
Actual Death Residence: Europe

That his SSN was issue in New York State suggests he was born there; but this is not necessarily so.

Henry PIERS
Birth Date: 10 Nov 1896
Death Date: Aug 1979
Social Security Number: 370-07-1915
State or Territory Where Number Was Issued: Michigan
Death Residence Localities
ZIP Code: 49423
Localities: Holland, Ottawa, Michigan
Death Benefit Localities
Zip Code: 49423
Localities: Holland, Ottawa, Michigan

At:
http://members.cox.net/drhelmholdt/g000134.htm#I00020
This is also Hendrick Piers.

Recently, I have been looking at a Piers family in New Brunswick, Canada. They arrived there from the US in 1783, probably from New York. The head of the family was a Henry Piers, but I see no member of the family that might be the one you seek.

I looked at the 1901 and 1911 Canadian censuses, but found nobody named Henry. I only searched for 'Piers', and not the several possible variants in spelling.

If you know when and where he married, you should be able to apply for a copy of the marriage record. These often had things such as age, place-of-birth, parents, religion, etc. This information would be very useful to you.

If you find any specific clues, let me know.

Thomas