Generally speaking, yes you need to lamp with the brand. However, OPI, the second best brand, cannot even make their lamps to cure correctly. They have been re-enginnering their lamp. It should actually be done by now but I haven't look into it. Its been almost a year now.
So what the heck has been going on all this time with gels? Well, everyone is pretty much curing their gels to 50%, to which gels become hard. But gels need to be 90% cured so that it doesn't cause allergies, among other things like strength.