Both are quite far away for a day trip and ferry timings make it especially unlikely that you could coordinate a day trip to either place. Staying overnight would give you a lot more time to enjoy your destination especially since these are very nice places.
Ko Lanta has loads of accommodations and Ko Adang has lovely new park bungalows or you can camp.
From Phuket day trip suggestions would be to Ko Tapoo (James Bond Island), Ko Phi Phi, one of the remote beaches in Northern Phuket, or to Coral or Raya Island (off the southwest coast of Phuket).
I don't really think Lanta is a daytrip. By the time the ferry arrives via Phi Phi, you will really have to start heading back. Google ANDAMAN ISLAND HOPPING ferry schedule for details. Spending a night or two makes much more sense.
If you google TIGERLINE ferries you will find they have a Phuket to Ko Lipe service - not sure if the first part to Lanta (or maybe Pak Bara) is by regular ferry or by minibus - but the point is it will take all day to get to Lipe starting very early - and then another short hop across to ADANG. So visiting Adang could burn 3 days at minimum.
For daytrips out of Phuket, Phi Phi, Coral Island, Ko Racha, Khao Lak, fabulous Phang Nga Bay are the go.