Just asked my colleague who is a trade marks expert (Jason Rudkin-Binks). He said this:
Trade marks cannot be similar to other trade marks – that rule is generally applicable in all countries. Similarity is gauged phonetically, conceptually and visually – lucid and lewcid are phonetically identical and so too similar to each other – adding NZ will not help as it just sounds like you are the New Zealand arm of the business – if you used it you couldn’t expand to any country where the Canadian company had traded first. I’d choose something different.
Feel free to contact him at firstname.lastname@example.org