1901 Census London

[amondg]

Double check the findings of your friend.

As they were in Liverpool 1911 they may have checked that area only. 

[amondg]

Have you tried the Jewishgen website

[cockney rebel]

Very elusive, I think you are right that the name was either mis-recorded or mis-transcribed.
What was David's profession ? It would have been given on his death certificate.
With an occupation, it would be easier to do a blanket search.
I was amazed at the amount of returns for "Lazarus"...and how many spelling variations!
Hope one day it all clicks into place...
Rebel

[steve62]

He was a boot maker and childrens MC also states the same.
steve62