Frillish are fairly adaptable, being partly ghost-types. (Ghost-types tend to be more resilient to environmental changes than most pokémon, except in the case of light.) So yes, absolutely, they will do just fine in lakes.
That having been said, frillish are also fairly easy to care for. To start, yes, they must have a body of water to rest in at all times. Although the salinity of this body of water doesn’t entirely matter, the temperature does; be sure that the temperature of the lake doesn’t drop below freezing … or, in other words, don’t let your frillish be in the part that freezes over. Otherwise, the fluids in her body will also freeze, which won’t necessarily kill her but will be massively unpleasant. Conversely, allowing her to dry out (by neglecting to give her water) results in a deflated frillish. This also won’t necessarily kill her unless she’s dried out for a long time and then salted. (Some parts of Asia consider frillish treated in this manner to be a delicacy, just as a fun side note.) It’s also possible to keep a frillish in a tank during the colder months, although this is only advisable if you have enough space and time to maintain one. Be sure to equip the tank with the usual tools a pokémon fish tank would use, including a filter/aeration system, plants, and a gravel bottom.
In terms of food, frillish are carnivorous (and do not consume the souls of the living, as is commonly thought). They often eat brine shrimp or plankton, both of which are available at most pokémarts, either dried and canned or shaped into a cake. (Simply break off pieces of the cake form as per instructions on the package.) Luckily, a number of fish-like pokémon share this same diet, so it’s not that difficult to find this sort of food for your frillish, but if push comes to shove, a generic water-type poké kibble will do just as well. Cleanup is not necessary unless you keep your frillish in a tank, at which point, clean her tank once a week at the minimum. (Remove all food debris and feces, cycle the water, add water treatments, and clean off any grime or algae buildup. The whole process may only take an hour.)
The hardest part of frillish care lies in keeping her enriched and entertained. Frillish are ultimately social creatures, and many females will want one or more male partners. As such, try to raise yours alongside your other pokémon. If you have a water-type, this will be even better. If you have no other pokémon, consider adding a male frillish to your home to help maintain your frillish’s mental health. Otherwise, provide your frillish with toys (anything light that she can carry or float—particularly waterproof balls or other waterproof toys), and be sure to train her for at least an hour a day, as per usual with most pokémon. Luckily, most frillish aren’t particularly aggressive or mischievous in low numbers, but nonetheless, always be on high alert for any poltergeist activity out of your frillish.
Best of luck!