Currently, Focus Lenses can be acquired through completing Sortie missions, and can be traded between players, while Greater Lenses can be crafted with a blueprint, or bought with Platinum from the market.
This is essentially the same thing the players talked about in the Steam post with the addition of crafting them.
Every 30-40 minutes there is a new alert. It seems quite random at first, but that's because you only see alerts of missions you already have access to.
In Warframe Developer Livestream #5 they talk a bit about how alerts are generated, at 59 min. Alerts are randomly generated, except for the once started after the life stream.
The Stalker spawning is completely random, it can happen to almost anyone at any time.
The reason I say 'almost everyone' is because you need to have killed at least one boss since the last time you were Stalked before the stalker can enter one of your games.
The first time I saw the stalker I was playing by myself, and I was relatively new to the game. I doubt I had any last hits on any bosses at that time, though I had beaten some by playing online with others who did the killing for me.
So other than the initial condition of having to beat at least one boss in your entire career, the stalker can spawn at any time, in any game mode, on any player.
Best Answer
From this Steam post there appear to be three good ways to obtains lenses:
They mention that you can purchase even better lenses from the market as well.
The Wiki also states:
This is essentially the same thing the players talked about in the Steam post with the addition of crafting them.