The side coached by Adam Barradell drew with Aston Villa last weekend but were beaten by the Hammers at Rush Green this time around.
Tomas Jonyla set up Chukwumeka Obi to break the deadlock 35 minutes in and that's how it stayed, to leave the young Foxes seventh in U18 Premier League table, on 24 points from 17 matches.
Crystal Palace are next up for City on Saturday, an 11am GMT kick-off at LCFC Training Ground.
The details
City: Marson, Aideed (Sutherington 59'), Diallo (c), Adedeji, Toko; Colangelo-Allen (Simons 82'), Manyumba, Lawrence, Boothe (Corden 66'), Owusu, Fletcher (Anugo 59').
Unused sub: Stretton.