Swimming during your period can be tricky, especially with cloth pads. Pads in general aren’t ideal for swimming because they're worn outside of your body, and will absorb any water they come into contact with - leaving limited room to absorb your period.
Since washing in water is how you get Lunapads clean, any menstrual flow already in your pad could seep out into the pool when you get in, too. If you have a light flow day, or are planning a quick dip in a lake or ocean, this is less of an issue - but since Lunapads attach with wings that can be seen from the outside, you probably won't want to wear them in your swimsuit.
Some people find the blood temporarily stops flowing while swimming because the water pressure holds it in, but only to a point. Once you get out of the water, all bets are off. It *will* start flowing again.
We recommend The DivaCup for swimming!