Can it be done? Yes!
Should it be done? Probably not.
The easiest and typically the best option is to build the level editor into the main app. This way the level editor will have access to all assets that the main game does and you’ll be able to create a “test your level” feature with ease. Also, this way the user doesn’t require Internet access or some special tricks to transfer the levels that they’ve made in the level editor to their local game.
Adding a level editor into the game shouldn’t increase the game’s size by much. I have created a few such games and all the level editor required was: 1) a few additional Lua files for ~100-200KB in total, and 2) a single new image sheet with scaling variants for ~3-5MB in total.
A level editor shouldn’t require much in terms of hard drive space. The most important factor with level editors (for users) is accessibility, i.e. is the level editor easy to find, is it easy and pleasant to use? If you force your users to download an additional app to their device just to make levels, then you are setting a high bar for anyone wanting to even try it out. Then, in order to play the levels that they’d make, they’d need to somehow transfer the levels to their game, etc. You’d basically be shooting yourself in the foot.