That's a big bag...I've only stayed at one hostel (the Shelter City in Amsterdam), and it had the narrow half-size kind of lockers you'd find at a gym shower room or school. It held my REI Alpine backpack just fine, but it's about half the capacity of yours.
And yes, you should bring your own lock - I had to use mine. I'd recommend a combination lock, so you don't have to worry about carrying/losing keys (just don't forget the combination).
If you're worried about securing your pack, check out Pacsafe's line of theft prevention devices:
I've used some of their gear, including the money belt and Prosafe retracting cable lock. I've also got their Wrapsafe backpack securing lock & cable on order, since I'm bringing a 4,300ci Gregory Baltoro pack to Europe next month to do a two-month pilgrimage in France/Spain. Good luck!