Hi OP, from the Lizard you will be close/ish to the Cornish Seal Sanctuary at Gweek, Flambards theme park in Helston, Falmouth (National Maritine Museum, Pendennis Castle, beaches), Via Ferrata in Penryn (climbing in an old quarry with a fabulous cafe), Marazion and St Michael's Mount (think you need to book the mount in advance and it's only open on certain days), the Minack Theatre (and stunning beach) at Porthcurno, Geevor Tin Mine at Pendeen, Lands End (just to say you've been, its quite tacky apart from the views) you could walk from Sennen Cove, Cape Cornwall (cove, hot chocs etc in car park or at the golf club) St Ives (get the park and ride train from St Erth).
There is Go Karting and Paradise Park in Hayle, Country Skittles just outside Hayle, wildlife spotting boat trips from Penzance (Mermaid or Marine Discovery), swimming at the Jubilee pool in Penzance if it's nice weather, sand dunes/beaches in Hayle and Gwithian. You can park at Godrevy (NT) and walk round the cliff path to a nearby cove where there are often LOADS of seals on the beach. Tehidy Woods (again a nice tea room).
Sorry for epic list but there is plenty to do, you'll have a fab time.