The lilies were knocked down by the rain.

Literal

Lilies [subject-が] rain [because-のために] knocked-down [passive-されてしまった].

百合 here means 'lily' (the flower), not the name. 打ち倒されてしまった combines the compound verb 打ち倒す ('to knock down') in passive form with てしまう for regret/completion. のために marks the cause.