My rule of thumb is that the only stupid question is the one you don't ask.
Answers, on the other hand.... ?
Anyway, i am not running cm10 right now and don't know if it offers LTE or how to change your network mode on it if it does. I don't have lte here so I didn't look when I tried it out.
To start with though, I have read over and over again where people are describing problems with getting or retaining lte on this phone. Their phone struggling to maintain an lte signal, phone right next to them on solid. Try using this site to see if it is even in your area to begin with.
Coverage Maps | 4G - USA - Sprint | Sensorly
On MeanRom, under settings/ click on Mobile networks and then you can click on Network mode. It is possible to be on cdma only but by default it should be in lte/cdma mode and supposedly would hook up to 4g if a version your phone was compatible with was available. In my case, ATT and Verizon have saturated the area with 4g.
Doesn't do me any good though. Sprint is really fairly challenged in it's coverage and signal departments, if you ask me. They say they are working on it, and that can cause problems in and of itself, but I haven't seen any good come of it here yet.
Also, one last thing, a stock rom will lie to you and tell you you have 3g all the time, I am told, whereas a custom rom will tell you straight what your signal is.
None of this precludes you having a hardware problem either though.
One thing regarding that I have read, is guy took off his back cover and slightly and carefully adjusted the contact pins on his phone to make better contact with the antenna built in to the back cover. I haven't looked at it, not sure how easy it would be to break it. I think he only claimed it helped his wifi though.