Zed is the pronunciation of the letter Z in the UK and some other Commonwealth countries (if not all of them), also the letter is still pronounced zed in abbreviations, and when spelling a word out in letters. I'm British (Scottish) and would never pronounce the letter Z as zee, under any circumstances.
Zee is the name of the letter Z in the US, and it's the same pronunciation in abbreviations and when spelling a word out in letters.
So both are correct!
As for LZ, you might find a pilot is the best person to ask. The answer might be different in your particular example if there is an internationally accepted pronunciation in the aviation industry. I'd like to think all pilots speak the same lingo! There's a distinct possibility that pilots might use the ICOA Spelling Alphabet, sometimes called the NATO Alphabet, to pronounce abbreviations - so that would be Lima Zulu. I am not a pilot, but I did find this link. Another possibility is that pilots would say "landing zone" in full, and perhaps might not abbreviate it.
In the UK, the police use the ICOA/NATO alphabet for abbreviations, and spelling out car number plates.