。
It's not a life-threatening illness.
Literal
Life [to-に] relate [like-ような] illness [copula-ではありません].
命にかかわる is a set phrase meaning 'life-threatening' — literally 'related to/affecting life.' 関わる ('to be involved with, to affect') takes に for what is affected. ~ような ('like, such as') attaches to a relative-clause-like modifier. A doctor-patient register sentence.