Hi,
Bit tricky this one, as you say Alfred died ~1843. So really the 1841 census (index) is required. Best is to send Kevan a Personal Message (PM) asking if he could do a special lookup for you. He may be able to transcribe from the actual info??
From 1851 Harwich index (HO107/1780) there are a LOT of Lambert, including:
LAMBERT   JEMIMA   6              ARDLEIGH         ESS   393   ARD
LAMBERT   JEMIMA   34            GT.BROMLEY   ESS   393   ARD
LAMBERT   FREDERICK10   ARDLEIGH    ESS   393   ARD
LAMBERT   ALFRED   25   ARDLEIGH                   ESS   373   ARD
LAMBERT   WILLIAM   22   ARDLEIGH                   ESS   373   ARD
LAMBERT   ROBERT   19   ARDLEIGH                   ESS   411   ARD
LAMBART   JOHN   81   LT.BENTLEY   ESS   161   RSY
LAMBERT   FRANCIS   57   WICKHAM MARKET   SFK   454   LBT
LAMBERT   ELIZEBATH57   FRESSIN                   SFK   454   LBT
LAMBERT   JOSEPH   18   RAMSEY                   ESS   454   LBT
LAMBERT   JOHN   24   RAMSEY                   ESS   454   LBT
LAMBART   MARY   17   LT.BENTLEY   ESS   456   LBT
LAMBERT   HENRY   30   RAMSEY                   ESS   437   LBY
LAMBERT   MARY   30   BRANTHAM   SFK   437   LBY
LAMBERT   HENRY   2   TENDRING   ESS   437   LBY
LAMBERT   THOMAS   7mnths   LT.BROMLEY   ESS   437   LBY
Ardleigh ARD Little Bentley LBT Little Bromley LBY Ramsey RSY
Certainly I would say the first batch look correct, as they are all Ardleigh. Would assume Jemima is correct, so Frederick and Jemima Jnr are from the second marriage, the others from the first marriage, that would tally with facts and dates given? As for the rest???
From 1861 Harwich (RG9), amongst LOTs of others:
LAMBERT   ROBERT   30   1096   37   ARD
LAMBERT   RHODA   32   1096   37   ARD
LAMBERT   RHODA H   1   1096   37   ARD
LAMBERT   ELIZA R   4   1096   37   ARD
LAMBERT   WILLIAM   32   1096   37   ARD
LAMBERT   WILLIAM   5   1096   37   ARD
Ardleigh; Little Bentley; Great & Little Bromley; Elmstead; Lawford
Again some possible useful ones from Ardleigh? No Jemima or Frederick. But Robert is now back with the others?
Good luck,
Geoff.