Lucy told Toz about Tasha's return, but after acknowledging it, Toz didn't do more. He knew Joshua and his family would be busy with their reunion, and Toz was busy with the sword technique he got from Stris.
After kidnapping Stris and taking his things, Toz had only had enough time to glance over them since the state of Pirate Haven and his intention to become Pirate King didn't allow him any free time. He only had enough time to train his mana now and then, so his void mana was steadily approaching the sixth level, but he didn't have any spare time to begin learning the techniques he saw in Stris' spatial items.
However, now that Toz had become the Pirate King and things in Pirate Haven were in control, no one could fault Toz for grabbing some time to train and grow stronger.
