The east Belfast MLA made the comments during a party conference in Enniskillen on Friday.
She told those in attendance: “Anyone who watched Sorcha Eastwood demolish Jeffrey Donaldson with his own words on Thursday’s Question Time can be in no doubt that Alliance can win that seat.
“Anyone who watched Jeffrey nervously drinking his water while she did, or heard the DUP attacks that focused intensely on Alliance at their conference last week, will be in no doubt that the DUP believe we can too.
“With boundary changes and party growth in places like east Belfast and the new South Belfast and Mid-Down constituency, there are significant opportunities, not only to retain the North Down seat but gain a team of Alliance MPs.”
East Antrim MLA Lyons, who is also Director of Elections responded: “Typical arrogance. Westminster seats are in the gift of the electorate, not Naomi Long.
"The Alliance Party’s disregard for the views of unionists will not be forgotten at the polls. Alliance didn’t call to exclude nationalists when SF collapsed Stormont over the Irish language yet when unionists are unhappy, the Alliance Party are straight to the microphone calling for unionists to be excluded from the Executive.
"People will judge Alliance on how they repeatedly act as Sinn Fein’s wee helpers but can’t find the strength to light up a building in solidarity with the Israeli people who were slaughtered in a terrorist attack, in case they offend their mates in Sinn Fein.
"Let’s also remember that the Alliance Party got it wrong on the NI Protocol. When we said it needed to be changed, Alliance stood with the EU, SF and SDLP calling for the Protocol to be “rigorously implemented”.
"Yet we were able to secure progress under the Windsor Framework and get a better deal for Northern Ireland.”
The interview on Question Time involving Eastwood and Donaldson was described as "spicy" by Ulster Unionist leader Doug Beattie.
Eastwood told Donaldson: “We didn’t like Brexit (but) we worked it and we made it happen.
"Do you know what? Our job is to govern, our job is to stand for election and do a job. If you don’t want to do the job, get out of the way.”
Donaldson, who is Northern Ireland's long-serving MP replied: “I took my case to the people in this constituency, as did Sorcha, and Sorcha can look down her nose at unionists all she wants, but I got a mandate from the people of this constituency to take the actions that I have taken.
“The politics of exclusion in Northern Ireland doesn’t work, and it saddens me that the Alliance Party, of all parties, are now talking about exclusion, excluding people (and) that unionists should get out of the way.”
Meanwhile, Sir Jeffrey has also shot down claims that a united Ireland will happen during his lifetime.
In an interview with the Sunday Telegraph, the DUP leader responded to Taoiseach Leo Varadkar telling RTE last month that it could be a possibility during his lifetime and that his party won't be "bullied" into a Stormont return.
He said: “I don’t think there is going to be a united Ireland in my lifetime.
“I think the people of Northern Ireland will continue to vote to remain part of the sixth largest economy in the world. And to be part of a nation that has influence right across the globe.
“Some in government seem to think that the way to get the institutions restored is to punish people and to basically bully people back into government. We don’t respond to that kind of behaviour.”