My mobile carrier is upgrading their network; must I replace my phone?

My mobile carrier is upgrading their network from 3G to LTE. I'm using a LG V20 phone, model LG-H915 to be precise. So far, I have been contacted twice by them, claiming that my phone and SIM card should be replaced because of this. They have even offered me a new phone, but I have declined since the model they offered is a cheap one. There are good reasons to change for a new device, that's true. For one thing, my current phone is running Android 8, which is, well, very outdated to put it mildly. The battery, which is the original one as I never replaced it, seems to be draining a bit faster as well, but it's hard to tell. However, I'm not sure about the network thing. I did a bit of research, and as far as I understand, the V20 does support LTE, so I should be fine with the new network. In fact, when I activate mobile data (I usually keep it deactivated unless I actually need it), I see a LTE logo appears, and if I check in the phone's settings, it actually says that the network is indeed LTE. From Settings-­>Network->Mobile Networks : From Settings->General->About Phone->Network : So, do I understand this correctly and in fact do not actually need to change phone (well, not because of the LTE network, anyway)? Or is my mobile carrier correct about this?