That may or may not work. I wouldn't attempt it unless I was on a TV show trying to win a million bucks.
Once you clear immigration etc, step out the airport front doors and walk/run to the little building on your left. That's where you catch the small plane.
If you miss the last panga to LCI, you may be able to charter a boat to make a special trip for you. Have a backup plan.
PS, budget 2.5 or 3 minutes in the Managua airport to find an ATM and get local currency. Last I heard, BCI has one ATM (do you want to rely on it?), and LCI has none.
If the fight time is at 2pm, you should check in at 12:30pm or earlier to make sure your seat, your baggage on the same flight and your earlier arrival (in case there are second or third plane). If you check in later, your possibility to lose your flight or your baggage arrives on the next day flight is bigger. i would travel next day on the first flight.
I think you'd be fine. Our 2:30 flight was at least an hour late, which seemed common, so I wouldn't worry too much, but I would have a back up plan.
The atm is a good idea to use in the airport before flying to the atlantic coast. Sometimes it will only give you 500s which are hard to find change for. I'd bring a bunch of small usd bills to use in case. Sometimes spending dollars you don't get the best exchange rate but it sure beats not having change.
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