Do you think Lillie will receive or catch another Pokemon, if so, what will it be?
My answer is yes. I could see her having a Cutiefly, Stufful, or Comfey. There could be others, but those were the first ones off the top of my head tbh.
I know Lillie still has a her fear to get over and it's a working progress, but she has made strides already. If Lillie can completely get over that fear (which I think she eventually will) and you combine that with her vast knowledge of Pokemon, I think she can be an awesome Pokemon Trainer! I'd really hate to see her go through the Anime with just one Pokemon. I like Shiron a lot and the relationship they're building, but I don't want to see wasted potential because I obviously feel like Lillie has a lot to offer. It also makes me wonder, with all the Pokemon that comes to her mansion, if she'd catch one those as well.
To be honest, I don't see Lillie catching (or receiving) another Pokémon, at least not until
very late in the series. The main reason is because of her fear. While she has made
a lot of progress toward conquering her fear, the fact that she had already bonded with Shiron when it was still an egg probably contributed to her being able to grab Shiron when it was in danger. She had already developed a "motherly" attachment to it.
It seems Lillie is more like Ash than she appears to be at first glance. Before Lillie catches another Pokémon, I think she has to work up the courage to (voluntarily) touch a Pokémon she already knows, such as Pikachu.
Don't get me wrong; I would
love to see Lillie get another Pokémon and really develop as a Trainer. Like you said, she has the potential to be an awesome Pokémon Trainer! However, I'm not sure that will happen until she has
completely conquered her fear, and I have a hard time seeing that happen until the Aether arc kicks off and we learn the cause of Lillie's fear.
Of course, I could totally be wrong about all of this, and I will be absolutely thrilled if I am.
If Lillie
does catch another Pokémon, then of the ones you suggested, I think Cutiefly is the most likely. Stufful might be out because of Team Rocket's stalker Bewear, and Comfey is apparently one of Alolan Nurse Joy's assistants, so I think it's out, as well.