As far as a I know, the lid is not really necessary for this style of dumpling at all. The only affect it will have is to increase the level of steaminess above the waterline, and very slightly prevent the dumplings from drying out. That is rarely a problem, especially if you flip the dumplings half-way through cooking.
Your not quite big enough lid should be more than adequate if you want to use one, as it will help the steam stay on top of the pot.
If you are concerned, you can improvise a more tightly fitting lid from aluminum foil Even if your foil is not wide enough you can link two (or more sheets together):
- Lay two sheets on top of each other, with their edges aligned.
- At one edge, fold it over about one inch (2.2 cm) or so, pressing down well at the fold line.
- Fold the one-inch fold over itself so it is now four layers of foil 1/2 inch wide, again pressing down well along the fold line.
- For a very good bond, fold the half inch seam over itself again, so you have a 1/4 inch overlap, again pressing well down the fold line.
- Open at the fold line edge like a book, creating essentially a sheet of foil almost double the width, taking care not to pull apart the extra folds of the seam you created.
If you need a triple width, you then lay another sheet on top aligned with the edge of of the first batch, and repeat the process.
Another improvised pot lid that is often helpful is to take a large dinner plate or charger that is heatproof, and lay it across the top—you just need one larger than the diameter of the pot; just make sure you use a towel or an oven mitt when taking it off the pot. Depending on your dishes, you may have one that will work well.