Why doesn’t my Electrum LTC wallet ask for password when opened?
Reason, not the same versions:
Bitcoin Electrum is at version 2.8.3
LTC Electrum is currently at 2.6.4, on their official website (electrum-ltc.org), which is a version released in May 2016 - most likely the version that you are using.
If your were to upgrade to the latest Github version at 2.8.3, you would be asked for your passphrase - like for the Bitcoin Electrum.
If you are not equipped to compile your binary on your system - then wait a few days/weeks, until Pooler makes the Windows or OSX binaries available on the official website.