Couldn't tell you. First iOS device, so not sure what that is. Basically any tweets that are appearing my timeline are showing up on the lock screen.
I don't want to disable them completely, but only show mentions, which is what is already selected in the Twitter app.
When you open the official Twitter app, navigate to the 'Me' tab at the lower right, and tap the cog icon near the top of your profile, you can access the app's settings. Under 'General', there's a setting for 'Notifications Timeline'. This doesn't control actual device notifications, it only affects what appears to you in the Notifications tab within the app itself.
But at the top of the Settings screen, it should say 'Accounts'—and below that is a list of the accounts logged in on your device.
If you tap on your account name, you should be taken to a page with a mountain of notification settings. The two that would be the likely culprits would be 'Other' which is about 1/3 from the bottom of this screen, or 'Tweets' at the very top.
'Other' is the notification that controls all the newer notifications Twitter uses that seem to be meant to drive engagement. Alerting you that your friends followed someone or something like that. A lot of people find that annoying.
'Tweets' is the notification that controls per-user notifications, so any accounts you've got Mobile Notifications turned on for will appear here. And every tweet they make will notify you. There may be a chance that this setting got switched on somehow for a whole bunch of people you follow, which would definitely make it seem like every tweet in your timeline was hitting your lockscreen.
Note too that you'll want to visit this setting screen for all the accounts you may be logged into, because the app respects the notification settings for each account. So if you've got a main account with all the notifications off, but a secondary account with all the notifications on, you'll still get a ton of device notifications from that secondary account.