The complex number \(z\) is given by \(z = 3 + \lambda \mathrm { i }\), where \(\lambda\) is a positive constant. The complex conjugate of \(z\) is denoted by \(\bar { z }\).
Given that \(z ^ { 2 } + \bar { z } ^ { 2 } = 2\), find the value of \(\lambda\).