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Sorry to hear you don't like your lock screen. You probably wouldn't want one of those lock screen apps anyway because most come with ads and those ads pop-up every time you unlock your device, so more to hate. Anyway I have yet to cross a device that does not allow the user to change the appearance of their lock screen so this seems a bit odd to me that you would be stuck with something that was unchangeable.
Let's start by trying to change what you have. There are a few different ways I've seen to modify the lock screen appearance.
The way with likely the most options is to open the settings menu and typing "lock" into the search bar. Then selecting "Lock screen" from the options. Under Lock screen look for Widgets or Clock style since that is what you're trying to change. Mine is a Samsung so my options and wording may be different than what you're seeing but for the most part Android is Android and these should be pretty standard options.
If you're not finding the options you're looking for in that location, there may be a way to make the changes you want from the customize screen. From the home screen pinch the screen by placing two fingers on the screen and doing the zoom out pinch move, moving your fingers together. This should zoom out of your home screen and show you all of your screens along with some options to add widgets, change your theme and do a few other things. Look under widgets for the clock widgets and see if you have any options to add a different clock to your lock screen. There may also be a settings option there with some options.
The last way to change your lock screen appearance would be to change your device theme all together. Or maybe not the whole theme all together as a lot times themes can be cherry picked. Theme pages are usually broke down in some way so that individual aspects of the theme can be chosen. i.e. wallpapers, fonts, icons and maybe a few others. Here you can look at different themes which usually show images of different aspects of the theme, like what the home screen will look like, what it will look like when a call comes in and so on. Perhaps you will find one with a lock screen that you like? Not sure about Moto but with Samsung's theming options 95% of everything costs. It may not be 95% maybe only 94.9% but if you search long enough you'll probably find something free. At least that is what I do.
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