Can I break one 30mg capsule into 2 x15mg ?

It isn't generally recommended to break any medication in half, unless directed by your doctor, because it can cause dramatic differences in the amount of time that the active ingredient is released within your body. If your doctor prescribed you 30mg, I would trust that he/she knows what their doing and simply take the medication as they directed you. If you have concerns about the difference in their instructions and the medication's instructions, then give them a call and see what they would recommend before doing anything differently.

It's not logical to break any type of capsules into 2 halves to take one half today and the other tomorrow, but it's ok if it was a scored tablet, or you should take the capsule of 15mg.
Usually lansoprazole course for Gastroesophageal reflux disease (GERD) is 8 weeks as prescribed only medicine (POM) and 14 days as over the counter (OTC).
Suddenly stopping the treatment after chronic use will cause rebound acid hypersecretion.
some studies says that chronic use of proton pump inhibitor (PPI) including lansoprazole will cause gastric carcinoids after chronic use