[Sprint LG G2] br0adband:
Sprint and Verizon's LTE technology requires the use of SIM cards because the device will connect to both the older network and the newer one at the same time. If you yank a SIM card from either carrier's device it will still connect to their CDMA-based network (with 3G technology) but to get their full LTE support it requires a SIM card.

Because of this, Sprint and Verizon devices released since roughly late 2013 have the potential - because they have SIM card slots - of being carrier unlocked. All Verizon devices come carrier unlocked with respect to the SIM card slot now because it was a part of the requirements they agreed to during the FCC bidding process to gain those new frequency allotments back in 2013 - you can go buy any Verizon phone right now, including the Droid Turbo (their flagship phone) and drop a SIM card in it from any other carrier and it'll work just fine without issues. It may not provide LTE support directly because of different LTE band/frequency support so that's what I'll explain below, just for the record, but it WILL work with any GSM SIM card right out of the box.

Sprint, however, wasn't bound by any such requirements and so their devices are not carrier unlocked but sometimes - please note I'm saying SOMETIMES they can be. The Sprint LG G2 is one of those times, and there are two basic ways to do it:

1) Either do all the necessary config/device adjustments to get the SIM card unlocked for use with GSM capabilities (very impractical solution and only useful if you absolutely refuse to use a custom ROM)

2) Use a custom ROM because all the work to unlock the SIM card slot for other carriers is already done for you by the developer of the ROM (or them using code that was ready to go). ROMs like CloudyG2 and others, once installed, offer the ability to use any GSM SIM card in the Sprint G2 without issues.

Having said that, the LTE aspect is where some have issues - Qualcomm "locks down" radio hardware based on the NV (non-volatile) firmware inside it and it's done that way based on the requirements the carrier sets forth. Sprint uses LTE bands (as noted in the post above) that are not directly compatible with T-Mobile's LTE bands - there's no overlap at all; if there were any overlap whatsoever you could feasibly get LTE to work with T-Mobile, but that's not the case with the Sprint G2.

The hardware in the phones is the same (with respect to the GSM capability and LTE falls under that umbrella), it's just that the radio hardware has been "locked down" to only use particular frequency bands. Theoretically it's possible to edit the NV and open up more bands (potentially supporting everything) but that's another thread altogether, literally, and has the side effect of potentially bricking the radio hardware if unsuccessful so people don't even bother with it.

Using the Sprint G2 with T-Mobile will get you HSPA+ capability that'll max out (theoretically) at 42 Mbps which is damned fast, plus HSPA+ offers better signal strength overall than LTE does and better building/structure penetration as well - and better battery life to some degrees (not like it was years ago when LTE hardware and software was truly unoptimized).

When I last had a G2 recently I was pulling about 38 Mbps down and 33 Mbps up in speed testing but I live like 2 blocks away from a T-Mobile cell site here in downtown Las Vegas with line-of-sight to the tower (no obstructions in between) and that's damned fast enough for me and most anyone. LTE is nice but it ain't everything... ;)

Suffice to say if you have a Sprint G2 you're not limited to just using Sprint, obviously - but LTE support will only happen if you use a carrier that overlaps onto the LTE bands/frequencies that Sprint itself uses. That basically rules out any carrier in the US since the remaining carriers of the "big 4" (AT&T, Sprint, T-Mobile, and Verizon) all end up reselling their network service to every other smaller carrier or MVNO - the other 3 carriers don't use the same LTE bands/frequencies so you'll have to be outside the US aka non-domestic to get LTE support. The Verizon G2 offers the potential to get LTE on T-Mobile because they do both share LTE Band 4 but it depends on the precise frequencies in use - more than likely you'll still end up with HSPA+ support more than LTE.

That should clear it up a bit for you...

ps

Next time perhaps take a look at the date of the last post in a thread - this was almost a year old since the last post so... things haven't really changed with respect to the Sprint G2 and LTE on T-Mobile; this info is found in other threads if you do some searching but hopefully you'll understand things better now with the info I provided.