Going into the final round of fixtures in a hugely competitive Pool 2, Pontypridd needed a bonus point victory over the Academicals while hoping London Welsh could get the better of London Scottish in the other fixture.
Lewis' side fulfilled their side of the bargain with a comfortable victory and when news filtered through of Welsh's win over Scottish, Pontypridd could celebrate reaching the last eight of the cross-border competition.
Wales Under 20 centre Garyn Smith did the damage with two of Pontypridd's six scores in an all-round impressive performance. The draw for the British & Irish Cup quarter finals takes place on January 27.
"The conditions were incredibly difficult but we scored some good tries and we delivered as a team," said Lewis.
"It was about controlling what we could do ourselves and that was winning and scoring four tries. We did that and I couldn't ask for anymore from the players especially given the deluge towards the end.
"There were some people looking to the London Scottish result and we were reliant on others. But overall, I think the way we've played against some fully professional outfits means we've deserved to go through."
The home side were always in control against an Edinburgh side who struggled to string any attacks together. Geraint Walsh opened the scoring and Smith's first try gave Pontypridd a 17-0 interval lead. The second half saw four more scores with Aled Summerhill and Owen Williams both adding to a penalty try and a 90 metre dash from Smith late on.
"It wasn't easy to handle the ball out there but I thought some of the rugby we played belied the conditions," said Lewis.
"It's a tremendous achievement to qualify. We've come through it and it's a testament to the players here who are determined and put a lot of effort in. We're now looking forward to a quarter final."
Pontypridd skipper Simon Humberstone, who kicked five conversions and a penalty, added: "It was really tough, towards the end it was some of the worst conditions I've ever played in.
"We're chuffed with the result. I said to the boys before we wanted a big performance and that's exactly what we got. We had a lot of young guys come to the fore, I think Garyn Smith is growing with every game and there are a lot of players coming of age at the moment."
Humberstone's tactical kicking was one of the main reasons for Pontypridd's success, the fly half controlling the game impressively.
"I think we used the chip, cross kick and up and under quite well, we didn't play as much rugby as we would have liked but conditions dictated that," he added.
"When you looked at our pool at the start of the competition with London Welsh, London Scottish and Edinburgh Academicals, you're thinking you have it pretty tough. It was a group of death but week after week, the boys have fronted up and it shows the strength in depth we have here. Away to London Welsh and London Scottish were definitely turning points for us, the performances we put in down there were very pleasing.
"We're very, very pleased with what we've done. I think we've shown over the last two years we can compete with the best sides. We've got a shot at another game now, it'll be a one off and we'll have every chance of winning."
Elsewhere, Aberavon got the better of Gala 11-9 at the Talbot Athletic Ground. In a tight encounter, a try for the Wizards from full back Jonathan Phillips proved to be the difference between the two sides.
Llanelli were edged out by just two points away to Connacht Eagles while Cross Keys were beaten 31-17 by Moseley.
In the only Principality Premiership fixture to take place, Llandovery downed Neath at The Gnoll. Jake Randell opened the scoring and second half scores from Sam Soul and Richard Brooks sealed the win.
For a full match report on Pontypridd's win click here.
British & Irish Cup results:
Pontypridd 43-0 Edinburgh Academicals
Aberavon 11 -9 Gala
Connacht Eagles 12 - 10 Llanelli
Moseley 31-17 Cross Keys
Principality Premiership result:
Neath 11-20 Llandovery