"No, it wouldn't prohibit him at all," said Brown. "Bear in mind that we're a quarter-shareholder in the Lions and we'll have some say in that too. Our view in that would be that if we're planning for success, and we've come out of a very successful World Cup, and Eddie is the right coach for the Lions, the arrangement isn't going to preclude that.
"We're not ruling it out. But it's quite a way away and there are a lot of things to happen before then and it's not entirely our say either. This is fundamentally about England, but no, it doesn't preclude a Lions situation if it were to occur."
Jones, who also ruled himself out of involvement with last year's Lions tour because of his desire to concentrate on his day job, would be the strong favourite to succeed Warren Gatland if England enjoy a successful World Cup.
But the Australian said he is "not arrogant or presumptuous enough to think I would be offered the Lions role".
"It is not really part of my rugby history," he said. "I would see that as being consequential of coaching well, so it is not something I really think about or worry about."
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The contract extension for Jones is deserved reward for a remarkable run of results that has seen England win 22 out of 23 Tests, including two Six Nations titles.
It is also a key feature of a new succession plan announced by the RFU, which will see the governing body also appoint a head coach at the end of the 2019-20 season.
Brown said it is critical for England to change the previous haphazard approach to appointing head coaches.
"In the past we have tended to have this disruptive reset of our coaching teams at the end of every four-year cycle," Brown said. "We wanted to avoid that and also have a smooth transition into the next head coach."
How the succession plan will work in reality is less clear-cut. Jones insisted that while he was head coach he would remain in charge, but that raised questions about how it would work if the RFU go for an international heavyweight to replace him.
The RFU Professional Rugby Department has already begun assembling a long list of potential successors, which will include Exeter's Rob Baxter and Mark McCall of Saracens from the Premiership.
The leading candidates with international experience would include Andy Farrell, currently Ireland defence coach, Warren Gatland, Joe Schmidt and Montpellier head coach Vern Cotter.
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It appears Jones' role in the transition period will be a flexible one.
"We've thought about how that would work," Brown added. "The whole agreement we have with Eddie, and it's important we got this right, is that we will discuss it at that time. We agreed with Eddie what's the best thing for English rugby, we worked out what that option was and put it in place."
To avoid the confusion that followed England's pool-stage exit from the 2015 tournament, which ultimately led to the departure of Stuart Lancaster and his coaching team just a year after they had all signed six-year extensions, it also contains a cast-iron break-clause for performance at next year's World Cup.
It is understood that Jones' extension will be terminated if England do not reach the knock-out stages while a quarter-final exit would also come under severe scrutiny, with the manner of the defeat likely to be decisive in whether he stays on.
"There are always key objectives and targets you have to deliver and if you fail there is inherently a performance element," said Brown, about the break clause. "But we've been quite explicit given the nature of what this is about and given the focus we've had, pretty much from Eddie's appointment, to get back in shape to win the 2019 World Cup. So it wasn't a difficult discussion.
"We looked at all various situations in the past, and observed others as well, and it seemed that (Lancaster deal) didn't work particularly well, clearly.
"That is some of the reason why we were clear about the performance break clause as well. And that is what this is all about at the end of the day, winning. Learn from the past, learn from good practice and think differently too."