Complex sentence: The union between Arsinoe II and Ptolemy Keraunos was purely political as they both claimed the Macedonian, Thracian thrones and by the time of Lysimachus father's death his power extended to southern Greece.
Split into simpler sentences: The union between Arsinoe II and Ptolemy Keraunos was purely political as they both claimed the Macedonian and Thracian thrones. By the time of Lysimachus'father's death, Ptolemy Keraunos' power extended to southern Greece.