The teenage right-back provided an assist for Divock Origi's stoppage-time equaliser in the dramatic 5-5 Carabao Cup draw with Arsenal at Anfield last week.
The Reds then went on to claim their place in the quarter-finals by coming out on top on penalties, with another Academy prospect, Curtis Jones, slotting in the winning spot-kick.
Williams is set to return to U19s duty under Lewtas' management on Tuesday when the young Reds take on Genk in the UEFA Youth League.
Lewtas' team sit top of Group E after three games and defeated Genk 2-0 away last time out.