The clash occurred after the Foyle MLA asked the minister how many jobs he had announced in Derry this year.
She raised the matter in the context of this week's employment statistics showing that '5.9% of working-age adults, including 7.6% of working-age men, in Derry are on a claimant count register'.
Mr. Lyons pointed to the work being carried out by Invest NI's office in Derry.
"She will be aware that there is a regional office there that is working hard to attract investment — with considerable success," he said.
The minister went on to claim that Derry enjoys a higher per capita state investment in jobs than anywhere else apart from Belfast.
"In the past five years, the assistance per head of population in the Member's council area has been £427. That is £427 per head of population. For context, that is above Antrim and Newtownabbey Borough Council; Ards and North Down Borough Council; Armagh City, Banbridge and Craigavon Borough Council; Causeway Coast and Glens Borough Council; Fermanagh and Omagh District Council; Lisburn and Castlereagh City Council; Mid and East Antrim Borough Council; Mid Ulster District Council; and Newry, Mourne and Down District Council.
"In fact, only one place has attracted more assistance per head, and that is Belfast. In fact, one of the lowest amounts has gone to Mid and East Antrim, so, if anybody should be complaining, it is me," said the Larne-based DUP minister.
This drew an angry response from Ms. McLaughlin who said: "Minister, you still did not answer my question: I asked how many job announcements you had made this year. You did not answer that. However, you have announced 1,600 jobs in Belfast this year.
"Why have the DUP Minister and his predecessors constantly neglected Foyle for jobs and university provision? What are you going to do about the unemployment crisis in my constituency? What is your response? How many jobs have you announced? You are not answering the questions; you are making snide remarks and being arrogant towards the people of Foyle who do not deserve it."
This provoked an outburst in turn from the Principal Deputy Speaker Christopher Stalford who loudly called the Assembly to order.
"Order. That is completely unacceptable behaviour. The Member has asked no fewer than five or six questions. When a Member is asked to resume their seat, they resume their seat. The Minister can answer whichever questions he chooses from the vast catalogue that was provided," said Mr. Stalford.
Mr. Lyons replied: "I take exception to the claim that I made any snide remark. I have simply set out the situation, which is that there has been an incredible amount of investment in the Member's constituency. It is second only to Belfast in terms of council areas.
"By the way, it is not the DUP or any DUP Minister who decides where jobs go; investors do that. As the Member can see, we have provided assistance there. I suggest to the Member that perhaps her approach is not helping very much and that she might want to work with others to address the issue."