I assume when you say "my Android" you're talking about a mobile phone or tablet running the Android OS? For this you'll want to get JMRI up and running. Well, technically speaking DecoderPro & PanelPro combined is the software suite, JMRI is the Java-based framework that it all runs on.
Before all that though, yes you would need to buy a throttle with the LZV100. A better question is "do I need an LZV100?", the answer to which is a resounding no. I have zero experience with Lenz systems, but judging by the specs and pricing this product is what we call a booster. Most starter DCC systems supply about 2amps, which is enough juice to run a handful of trains with ease. When 2amps doesn't cut it anymore, you add a booster to your layout (generally they're 5amps). The existing throttle will generally still plug into them, just the old 2amp power supply is bypassed. Basically unless you plan on running ops sessions with 10 buddies on day 1 you don't need 5amps.
Lenz isn't really all that popular on these boards to be honest, most people use either Digitrax or NCE. Both are very good and a decent starter system can be had for roughly $150. From NCE you're after the PowerCab (not PowerPro, that's a booster), not too sure about the Digitrax equivalent. Lenz is also not too well supported with JMRI unless you have that booster you mentioned.
As for connecting things up to JMRI that's a whole topic in itself and highly dependent on what system you have, but I can tell you how to get your Android device connected because that's thankfully very easy (once you have JMRI and DecoderPro running). Your first step is to have either A. a wireless NIC on the computer that will be running JMRI, or B. a router on your home LAN that has wireless (obviously your computer would be connected via ethernet if you're going with option B instead of A). From there you download
Engine Driver from the Android store and run it. Back on your computer there's an option in DecoderPro to start the WiThrottle server, and once done a little window will popup showing the IP address and port that it's broadcasting on. There's a bunch of settings you can adjust from this window but the default ones should work fine unless your router is overly restrictive or you have a firewall on your computer. Now go back to your Android device and you should see the IP address and port listed on your computer showing up as a discovered server. Select that and the next screen will be your controls.
You can type an address in, but if you've already set up your loco roster in DecoderPro (which you should do) you can just select which train you want to control from the list.
Here's a video of me driving some trains on my test layout using just JMRI. The control panels you see on the laptop screen are exactly what you get on an Android device. I recommend watching in HD on Youtube so you can actually make out what's on the screen.
[youtube]1F6A7ik3o14[/youtube]
