The lifeline subsidy does not come from your income taxes, but from a fee charged to telephone subscribers. This is used to make sure that poor people can call 911 and can participate in our society sufficiently so that they can get a job, go to school, and make use of government services that were formerly only available by phone or personal visit.
These days, getting a job requires use of the internet and you can't really hang around the library for the entire time you're trying to get work. So, it makes sense to give poor people some basic connectivity.
I believe the actual motivation behind this move is the same one that is behind making it more difficult for poor and disenfranchised people to vote - even though there is no evidence of significant voting fraud in the USA: Poor folks and minorities might vote Democratic. Suppression of the Black vote has historically been an important part of Republican strategy, this is just one of many reports on that issue. Having gerrymandered them into the most odd-shaped electoral districts, it becomes time to make sure they can't get news online or participate in democratic discourse.