An eGo should be fine with LR atty/carto...I use them all the time on mine. It means the contact is not good. I get this issue with my KGO fat-batts quite often. Two solutions.
1. Take a straight pin and find the side air holes above the atty threading. Stick the pin sharp end into one of the holes and pry downward. Then do this to the other airhole. You are trying to get the pin to hit the centerpost which is what makes contact, but it is too flush with the outer ground-threads. You are trying to slide this center post so it is more exposed out of the bottom by about 0.5 mm, maybe even less. This will generall make the contact possible and the carto or atty will vape.
2. Same problem, different solution. Take a pair of wire cutters, and cut about 1 mm off the end of a paper clip. Put this little piece on the center of the battery centerpost. Then screw the atty on, making sure you don't have the piece of paperclip hitting the side wall around the batt centerpost. I just did this with my KGO, which has a tendency to by fine with a new atty/carto, but pushes the atty/carto centerpost up when its screwed in. Fine for the first vape, but if I remove and reattach the atty/carto, now the centerpost is not contacting. This is also a problem in getting the KGO batts to charge.
3. Get a 510 extension piece.
madvapes has them:
510 Battery Extension
Often this piece will make better connections between the atty/carto and the batt, but I have had to slide the centerpost on these sometimes too. I think what you are seeing is becoming a growing problem with general quality control in battery connector specs. Glad you said this, as I was under the impression this was limited to eGo clones, like the KGO. Seems eGos also have this issue sometimes. If it is new, I would contact the vendor and get it replaced, as if this was the problem, charging could become an issue too.