As I understand it, the door in question is the original door and has never had a locking mechanism installed – it has always been a free turning handle or knob to gain entry.
Assuming that's correct – I believe your only course of action is to have your proposal(s) placed on the Agenda at the next meeting so it can be voted on by owners. Contact your Strata Managers to have your proposal listed. Canvass other owners and get them to attend the meeting or get proxies from them, in your favour, if they can't make it.
If the original locking mechanism has been removed or has failed to work properly, then the EC has a responsibility to maintain the locking mechanism in good working order.
As a Lot owner in a smaller strata complex, I understand that some EC's (possibly only 2 or 3 people) think they control the entire complex. This is not the case because their sole obligation is to represent the Owners Corporation (which is you and other owners) and they are required to look after your collective better interests. Don't ever be deterred by them.
As mentioned in previous Posts there's lot's of things the Owners Corp could approve, but it all comes down to money and the amount of dollars you have in your Admin & Sinking funds. If you don't have enough, a Special Levy will be placed on all owners to fulfill the financial obligations. These extra levies can & will place hardships on some – so tread carefully & chat with neighbours first.