Both teams have the benefit of the dominant Mercedes engines, if not the budget available to Renault-powered former champions Red Bull, and have been closing the gap in recent races.
Force India, whose upgraded 'B specification' car made its debut at the British Grand Prix on Friday, are fifth and 24 points adrift of Red Bull in the standings while Lotus are two further behind.
"It looks lean and mean," said Force India team co-owner Vijay Mallya of the new car.
"Today was the first outing... I think we still have to optimise the package that we have, there will be the inevitable upgrades that will come. So we are hopeful of having a strong second half of the season.
"Red Bull are 24 points ahead, Lotus are breathing down our necks. Fine, we are used to that. But I wouldn't be overly optimistic if I said that we are targeting fourth in the championship this year."
Lotus chief executive Matthew Carter said his team felt the same way after outscoring Red Bull, who have yet to stand on the podium this year and have been critical of their engine partners in the last two races.
"I think we are definitely targeting fourth as well so it will be interesting to see how the rest of the season pans out," he said.
Champions Mercedes have a huge lead in the constructors' standings but Ferrari and Williams are also well ahead of the rest.
Force India's Nico Hulkenberg was eighth in Friday's second practice, with Red Bull's Daniil Kvyat and Daniel Ricciardo fifth and sixth.
Hulkenberg, who won the Le Mans 24 Hours sportscar race last month with Porsche, sounded less convinced by his team's optimism.
"I don't know," he told reporters. "It really depends where we put ourselves with this package... it's really hard to tell. I think the focus at the moment should be to put it on and learn as much as we can this weekend."
(Reporting by Alan Baldwin, editing by Ken Ferris)
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