So that he wouldn't miss the train, he left home early in the morning.
Literal
Train [to-に] not-miss [so-as-to-ように] he [topic-は] morning early home [object-を] left.
~ないように ('so that X won't happen') is a purposive negative — the negative plain form 乗り遅れない + ように. The alternative ~といけないと思い (worry-based framing, 'thinking it would be bad if') gives a similar meaning through different grammar. ~ように specifically marks purpose, while ~と思い marks a reason-through-thought.