No – this not problem in internet connection . Read please this small “top of the iceberg” https://stackoverflow.com/questions/40431384/pip-install-not-working-debian
pip 1.5.6 in apt-get repository for raspi python 2.7 is old, and not have new TLS protocol. But for pip upgrade >1.5.6 we need to do a lot of interdependent actions, as a result, a lot of things will stop working.
The best thing to do for LS : install SD with EZ Wifibroadcast, connect ethernet port to router . And try install pivideo:-) And after that write How-to.
EZ wifibroadcast is great project and Picapture must supplied them as described: https://github.com/bortek/EZ-WifiBroadcast/wiki/AddOns-~-HDMI-in-Cards