Vector Algebra: JEE Main 2020 Mathematics question

If $\overrightarrow x$ and $\overrightarrow y$ be two non-zero vectors such that $\left| {\overrightarrow x + \overrightarrow y } \right| = \left| {\overrightarrow x } \right|$ and ${2\overrightarrow x + \lambda \overrightarrow y }$ is perpendicular to ${\overrightarrow y }$, then the value of $\lambda$ is _________ .