The company increased its offer to $0.43 a share, which values DMC Mining at A$46m ($38.2m).
Meijin Energy Group offered the same price in what is becoming a takeover race for the West African iron ore explorer.
Cape Lambert initially offered A$40m ($33.2m) before increasing its offer last month to A$.50 a share ($.41), or A$43.3m ($35.7m).
Meijin also increased its offer from 41 cents a share to 43 cents a share.
DMC Mining’s key asset is an 80% interest in the Mayoko iron ore project in the Republic of Congo, which has an exploration target of 0.9 billion – 1.3 billion mt.
Cape Lambert holds a 35.45% interest in DMC Mining.