Why am I not getting LTE data?

I currently own an iPhone 5s that was originally from Apple and the person chose Verizon as her carrier at apple. I have T-Mobile, and they told me the phone will work. It does, i'm on the network with their SIM card. I'm supposed to have 4G LTE data but I keep getting E. It is NOT because of the APN. T-Mobile checked that and it is the same. Apple told me Verizon might need to do an 'internet unlock' to get the LTE to work. But I saw that Verizon iPhone 5s are unlocked to work on any GSM carrier. Should my friend call tech support? I don't understand how some people get the LTE the same way I did but I don't. I also got 4G today for around 20 seconds but it went away. How can I get the LTE back

At least from what you've said an "internet unlock" is different from a phone unlock (which it already is, as it came from Verizon to T-Mobile). You should make the necessary enquiries yes.

Also it could be a matter of location, in that you are in an area where T-Mobile doesn't have LTE coverage.

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