There is a way to connect two non-Thunderbolt monitors to a Macbook Pro (Early 2011). You just have to daisy chain two Thunderbolt docks together, where at least one of the docks has an HDMI out.
This is because each Thunderbolt device can demultiplex only one DisplayPort signal from the Thunderbolt signal. So to get two DisplayPort signals out of the Thunderbolt signal, you need two Thunderbolt devices.
I have an Elgato Thunderbolt 2 Dock and a Belkin Thunderbolt 2 Express Dock. My Macbook Pro is connected with a Thunderbolt cable to the Elgato dock. My first monitor is connected to the Elgato dock via the HDMI port. The Belkin dock is then daisy chained to the first dock using another Thunderbolt cable. I then use a Mini DisplayPort to HDMI cable to connect the Belkin dock to the second monitor. When this is all connected up, the laptop's display shuts off and the two external monitors work normally.
It's not a cheap setup, but second-hand Thunderbolt docks are a lot cheaper than they used to be. Hopefully this helps anyone else like me who is stubbornly refusing to upgrade their 8 year old laptop!