While Electrum allows adjusting fees to custom values, it does not allow creating zero fee transactions.
Was this a change in one of their latest releases, because I've done zero fee tx with electrum a while ago when I transferred some bitcoins to a paper wallet!
I am using Electrum 2.6.4 on Linux, and when I attempted to make the fee zero, received a message saying this is not allowed. I do not know when this was introduced.