When I searched on fultonhistory.com, I put the following in the search box:
brooklyn ny daily eagle 1886~~1887 and lambert w/2 hannah
I put this in exactly this way with a boolian search and came up with 3 hits- 2 of the piece I mentioned previously, and the one you found.
I found Edward A. and Hannah in the 1860 Census - no new children that had to be her's - (a Carrie too old to be Hannah's, who was not listed in the 1850 -maybe she was staying elsewhere at the time). So Lansing, Elizabeth, Mary and Ira B. were Elizabeth's, and possibly Carrie. The rest in the 1880 were Hannah and Edward's.
If you go to the pilot.familysearch site for the 1892 NY STATE Census - for Brooklyn, you'll find Ira B. LAMBERT with wife Alice L. and children Ira W., Frederick, and 2yo Gladys, in Ward 20, E.D.13. You can save this image right to your computer or print it out. Hannah J. is living in 1st Ward, E.D. 16, apparently alone.
In the 1900 Census Ira B. and Alice are living with their 2 surviving children- Ira Walton, and Frederick.
Using the great german genealogy group site:http://germangenealogygroup.com
on the NYC Grooms Index :
Ira B. LAMBERT May 2, 1872 Kings county
cert. # 749
Edward H. LAMBERT Jun 20,1884 Kings co.
Rufus LAMBERT Sep 9,1887 Manhattan
cert. # 73873
On NYC Brides Index:
Louise M. LAMBERT Mar 2,1899 Kings co.
On NYC Death Index:
Ira B. LAMBERT 61y May 10,1911 Kings
cert. # 9846
I.Walton LAMBERT 32y Oct 15,1912 Manhattan
cert. # 29638
You can order cert. copies from the photocopy unit of the LDS for $2 each, min. order $4.00. You'd need to give the Title and FHL Film # for each film the cert. should be found on. These are found in the Library Catalog on familysearch.org. You can download and print out the Request form from familysearch.org site (form #31768).
Kit in New Hampshire