Hello. With 3 Gallon Pico, I assume this is cube, I think your return pump should be enough to create the flow for your whole tank, if you still feeling not enough then upgrade to a higher GPH return pump. Note that LPS don't need much flow. For the filter, you might just need the bio media in the filter chamber, LPS need higher nutrient so you might don't need the machanical filtration. For the light, I recommend the bugget saving Hygger (30w) or Lominie, I have been using these lights for both my pico and frag tank and saw the coral growth happy with them. Or the Kessil A80 Tuna Blue will be your optimal choice.
Best!