Steel wool is already a good thing. Maybe first scrubbing it with dry steel wool, and then with wet one. Some time ago I used to buy damaged microwave ovens on Ebay, repair them and resell them. Steel wool worked well to clean, but you have to scrub very hard.
If you need lye, easy availible lyes are :
* Soda (Na2CO3) : availible as cleaning agent in drug stores (Schlecker ...). It is a lye, despite looking like neutral, because Natrium is very powerfull lye and carbonic acid a weak acid.
* Caustic Soda (NaOH) : Availible as Photo-developer at some chemists or photo labs.
Theese are probably bad choices, but for completeness :
* Pipe cleaner : A mix of Caustic Soda (NaOH), Saltpeter (KNO3) and Aluminium. When mixed with water it starts to boil and becomes higly caustic (both alcalic and oxidating). You may have to verify your age, to buy it, and you should wear protection googles while using it.
* Amonia (NH3) : Alcalic gas available disolved in water at some office shops for making blueprints (rare nowadays). Its is caustic to respiratory organs, so be carefull not to breath it in high concentrations.
* Potash (K2CO3) : A weak lye like soda. I don't know there to buy it, but you could make it yourself, if you have an open fire place or other sources of ash.
* Lime ( Ca(OH)2 or CaO) : Availible at the contruction shop (for mortar). Strong lye, thought you should wash it away before it sets. Here, you should also wear protections googles. And make sure, that you actually buy pure lime, and not mortar or cement.
If you can legally buy it, a very powerfully cleaning agent is also Hydrogenperoxid (H2O2). It easily dissolves rancid fat. Make sure, that you don't mix it with acid (vinegar), as a mix of oxidizers and acid is very corrosive to metal. Here in Germany, it is no longer availible, because of all the anti-terrorist laws, but I think in Czechia laws are more liberal with that things. You need a high concentration (~40%), so hair dye is not sufficient.