The Brazilian makes his Premier League debut for the Blues after completing the switch from Paris Saint-Germain on a free transfer last month.
Silva impressed in his first appearance for the club in the 6-0 win over Barnsley in the Carabao Cup on Wednesday night, despite only playing for 60 minutes.
However, Lampard has clearly seen enough of the veteran defender on and off the pitch to hand him the armband, with club captain Azpilicueta starting on the bench at the Hawthorns.
When asked what Silva adds to the back line, Lampard said: ‘Experience, qualities, leadership.
‘He’s not speaking the language enough to do it in that sense, but it doesn’t matter with someone like him he delivers it with actions and presence and how he is with people around him
‘He’s been a winner throughout his career and I want to see that with us.’