"Gallery" isn't a place, it's an app, so when you say messages to into the Gallery what this means is that they go into a directory that your Gallery app knows to look for images in.
Unfortunately where exactly an SMS/MMS app saves to depends on which app it is. Assuming that this is Google's "Messages" app you are using then on my device that app saves to Pictures/Messages in my internal storage (I just switched to that app and saved an image to test). So that's where I'd start looking, but if not it might be a case of using a file explorer and looking for a likely folder.
For what it's worth, my preferred gallery app (F-Stop) found this folder immediately. It might be that your Gallery app has a setting you can use to tell it to rescan the device or look in other folders from where it is currently looking - I've no experience of LG apps so am guessing here.
