. . . so how did I even manage to petrify the whole thing at once, then?
That's actually a good question since tiletypes and liquids only really work in rectangles. Did you just spawn a huge amount of lava over the lake? Also, have you revealed the map? You may have affected a larger area than you intended and just can't see it all. (I like to use "reveal hell" because it keeps me from accidentally unpausing while I have the map in a cave-in-ish, dwarf-unfriendly, or otherwise delicate state (Remember to unreveal before you save, otherwise its a pain and a half to fix (you have to hide the whole map with tiletypes then use revflood)))
One thing that I can think of to help fix your lake is that you can set the range on tiletypes really high (like "r 100 100") then "filter mat lava_stone" so that tiletypes will only affect tiles made of obsidian (remember to set it back to "filter any" afterwards otherwise you'll wonder why tiletypes isn't doing anything all of a sudden).
Also, if you haven't already, you should open tiletypes and type "help", and read through it. At the end, it says "See help [option] for more information", which means that you should type things like "help Material" (or "help mat" or "help m") and "help Shape" in order to get a better idea of what is possible.
Also, if you plan to do this a lot, you will save a lot of aggravation by adding keybindings like "keybinding add Ctrl-Q tiletypes-here" and "keybinding add Ctrl-W tiletypes-here-point" to your dfhack.init file. Its miserable enough switching back and forth, no need to do more of it than necessary.
Personally I'm just dreaming of the day that the whole tiletypes/liquids/changelayer/changevein/sources/etc. dance grows into a full-blown map editor.