Hard / hardly
'Hard' is both an adjective and an adverb.
      The table is hard (= adjective, meaning 'not soft' or 'difficult').
      She works hard (= adverb, meaning 'with a lot of effort').
'Hardly' is also an adverb, but it means 'almost nothing' or 'almost none'.
     She hardly works (= she does almost no work).
      I have hardly any money (= I have almost no money).
Late / lately
'Late' is an adjective and an adverb. There is also an adverb 'lately', which means 'recently'.
      I'm late (= adjective, meaning 'not on time').
     He came late (= adverb, meaning 'not on time').
     I've been working a lot lately (= an adverb meaning 'recently').