Villa struggled for large parts of the last campaign and relied on a late flourish to avoid relegation and finish 15th.
The Midlands side have fallen to narrow defeats to both Chelsea and Liverpool in the last two games, though Lambert is delighted with the performances his players have delivered.
"The progress is there for everybody to see," the Scot told reporters.
"That's what I'm pleased about. [If] we play like that for most of the season, we'll have a good season.
"Away to Arsenal, away to Chelsea and home to Liverpool. That's a big turnaround in a week for us. The intensity you have to play at in those three games, especially the two away from home, I've got nothing but praise."
Villa face Newcastle United at home in their next Premier League clash.