The teams go into the game with the series deadlocked after three draws.
"I'm happy with the gradual progress of my team," Lara told reporters on Thursday.
"We've made some steps forward in terms of getting on top of the Indians and they are now taking notice of us. Going into the last Test, I think we have a slight psychological advantage."
West Indies narrowly avoided defeat in the first Test in Antigua, their last-wicket pair surviving the final 19 deliveries.
The hosts also hung on for a draw in the second Test in St Lucia when India needed three wickets to win on the last day.
India, set 392 in 88 overs to win the third Test in St Kitts, finished on 298 for four.
"I don't think the momentum is with the West Indies," Dravid said. "I think the momentum is with us.
"On the last day at tea we were in with a chance to win, rather than them.
"They've played some good cricket but we've also played some good cricket. Brian's not going to say the momentum is with India, nor am I going to say it is with the West Indies."
POSITIVE RESULT
History suggests a positive result is likely at Sabina Park, with the last eight Tests there having produced a winner.
West Indies have won six of those matches, including the 2002 contest against India that also decided the series.
"Jamaica is a results ground. I remember playing India there four years ago and we were able to get a win," Lara said.
"We'll look for that. We'd love to win this series."
India, traditionally weaker away from the sub-continent, are aiming to secure their first series victory in the Caribbean since 1971.
"Let's not take anything away from the very good cricket we've played in the series," Dravid said. "We've not been known to be good travellers but we've played some good cricket and we've got to continue that.
"We would have liked to have had a result in our favour going into the last Test but that's not to be. We can't worry about that."
Squads:
West Indies - Brian Lara (captain), Chris Gayle, Daren Ganga, Ramnaresh Sarwan, Shivnarine Chanderpaul, Dwayne Bravo, Marlon Samuels, Denesh Ramdin, Jerome Taylor, Pedro Collins, Corey Collymore, Ian Bradshaw, Runako Morton.
India - Rahul Dravid (captain), Virender Sehwag, Wasim Jaffer, Vangipurappu Laxman, Yuvraj Singh, Mohammad Kaif, Mahendra Dhoni, Anil Kumble, Harbhajan Singh, Shanthakumaran Sreesanth, Munaf Patel, Irfan Pathan, Vikram Singh, Suresh Raina, Ramesh Powar, Dinesh Karthik.
(Writing by Ken Borland in Johannesburg)
