The team's cars arrived at Monza for Sunday's Italian Grand Prix direct from Belgium, where bailiffs had moved to prevent them leaving Spa after the Aug. 23 race.
Team sources said that dispute, part of a legal action brought by former reserve Charles Pic and one of several obstacles faced by Lotus this season, had now been resolved.
"I can guarantee you that we will be at Singapore. One of our sea freight containers has left, our air freight will leave next week. We will be in Singapore," Carter told reporters, referring to the 13th round of the 19 race season on Sept. 20.
"Yes, the financial issues are all over the press. everyone's aware of them," he added.
"We are working as hard as we can behind the scenes to get them sorted out, none of them have become terminal obviously. We are still here and racing and will continue to do that."
Lotus have been in negotiations with French carmaker Renault, who previously owned the title-winning team, for several months.
Red Bull's engine partners Renault are mulling their future in the sport, with the main options being taking control of a team or quitting the sport entirely. A decision is expected soon.
Questions about whether Lotus will make it to the end of the season carry an echo of last year, when both Caterham and Marussia had to miss races and went into administration with only the latter team surviving.
"The negotiations are going on behind the scenes, I'm hopeful that is going to secure our future one way or the other," said Carter.
"We have more than one option going forward to secure the future of the team.
"As far as the rest of the races this season, we have a budget in place and we will operate to that budget and be at all the races."
French driver Romain Grosjean, who finished third in Belgium, said everyone at the team was waiting to see what happened.
"Hopefully the good news is coming," he said.
Grosjean was seventh fastest in Friday's second practice with Venezuelan team mate Pastor Maldonado eighth.
(Reporting by Alan Baldwin, editing by Justin Palmer)
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