Jesus talks about losing your life for his sake and finding eternal life (Luke 9:23-24). Is this referring solely to spiritual death?
Contextually, Jesus had just finished informing his disciples about his upcoming physical death (Luke 9:21-22). The following verses (vs. 25-27) make implicit references to death by persecution in that Jesus speaks of “gaining the whole world” (including keeping one’s physical life?) and yet forfeiting himself (or his soul – Matt. 16:26) due to “being ashamed of me and my words” and thus keeping quiet and avoiding fatal persecution. Verse 27’s prophecy of some of Jesus’ disciples still being physically alive when the kingdom of God comes clearly speaks of physical death.
For these reasons, it’s reasonable to conclude that Jesus’ statement “whoever would save his life will lose it” is a reference to saving one’s physical life by not confessing their Christianity to avoid persecution will eventually result in their condemnation to hell and the loss of their soul. His statement, “…whoever loses his life for my sake will save it” would refer to being physically killed because one refuses to renounce or keep quiet about their Christianity, and thus saving their eternal soul by avoiding the spiritual death of hell (cf. Rev. 21:8).