The Livestrong series was a series of bikes which price included a $50USD donation to Lance Armstrong's Livestrong Foundation. Hence the 'Livestrong' decals on these. Available from 2011 until the 2013 model year.

Trek Introduces Livestrong Series of FX Hybrids - Bikerumor

And:
Trek Introduces Livestrong-Themed Bikes | Bicycle Retailer and Industry News

Trek's archive page for the 2012 FX model:
2013 LIVESTRONG FX - Bike Archive - Trek Bicycle

Here's the BikePedia page for this bike model:
2012 Trek Livestrong FX - BikePedia


There was a Livestrong Madone 6.9 Pro available in 2009, according to one source, but that's just one comment- there are no other references to that one.

Livestrong Madone 6.9:
Lance Armstrong's Trek Madone 6.9 Livestrong - BikeRadar

Add: There was also a Livestrong 9th District model available: here's the Trek archived page for that:
2012 LIVESTRONG 9th District - Bike Archive - Trek Bicycle

BikePedia has a list of several sizes of this last model: And their values on the used bike market...
BikePedia

Trek archives home page:
2014 Bike Archive - Trek Bicycle

There was a recall of Trek bike models in 2012:
"Trek Bicycle is recalling about 27,000 FX and District bicycles because the bolt securing the seat saddle clamp to the seat post can break, creating the risk of a crash. "
Recall: Trek 2012 bicycles?seat can disconnect from post

So that narrows the bike down to being either a Trek FX or a 9th District model. :-)

Lastly, here's one for sale in Alberta right now:
FX Trek Livestrong road bike 2014 | eBike | Edmonton | Kijiji