EE blocked my stolen phone's sim, will this prevent Lost mode from taking effect? I had my iphone 6s plus stolen in a nightclub at the weekend, I activated lost mode straight away but the phone was offline. I then phoned EE to report the theft and they blocked the sim, but I've since realised that the phone has to connect to the internet in order for Lost mode to take effect and lock my phone and enable tracking to occur, so have I played into the thief's hands by having the sim blocked?
If you phone was stolen (and you didn't just lose it) you did the right thing having the sim blocked because it would also work in any other phone - once in possession they would be able to remove the sim, insert it into any other device and you would then be liable for any costs which occur.

Assuming that your phone was protected with a passcode, anyone trying to switch on the phone would not be able to access its content or reset the phone to keep for themselves or sell on. 
However, due to the difficulty thief's have trying to re-enable locked phones, its most likely that your phone will have already been taken apart and sold for its parts. 

If however you had just misplaced the phone and it was in fact not stolen, then with the phone being offline already, there would again be very little else you could have done anyway. You can still put it in lost mode, lock it, or remotely erase it. The next time your device is online, these actions will take effect.