Lactose is a reducing sugar.  This is due to

 Lactose is made up of $\mathrm{\beta }$ –D-galactose and $\mathrm{\beta }$ –D-glucose in which ${\mathrm{C}}_1$ of $\mathrm{\beta }$ –D-galactose and C₄ at  $\mathrm{\beta }$–D-glucose are involved in glycoside linkage.  So ${\mathrm{C}}_1$ of $\mathrm{\beta }$ –D-glucose is responsible for its reduction properties.