Yes its a lance, I looked this morning and its 1/8 inch pipe not 1/4 inch, I just hook up a shut off valve to the end of the pipe and weld a short tab on it to hook the welder lead on it to get a spark to light it, unhook the torch line from the oxygen regulator and hook up a line directly to the gas valve on the pipe, crank up the regulator to at least 80 psi or there about and keep the shut off valve off on the lance. Hook you welder stinger to the tab and turn on the welder and put a ground clamp on the work piece your torching, make sure you have plenty of fire proof clothing on and a helmet and touch the pipe to the work piece to get an arc and open the gas valve at about the same time, once lit you can unhook the welder stinger and the oxygen will blow the slag out towards you, it goes not up the pipe but outside it and the oxygen pressure blows the slag out of the shaft and hole your gouging, hence the need for the fire proof clothing, gloves and helmet, and keep contacting the pipe to shaft your blowing the hole through and your consuming the pipe as you shove it in so your getting closer to the work piece as you go. Once you have a hole started completely through, I usually gouge it out wider and then the slag will blow through the hole instead of back at you.
I think there are some video's on youtube about it, I've never taken a video of it, basically don't have enough around to shoot the video and its over so fast we seldom have time to worry about it.
Its very cheap and simple way to do it, doesn't take much, but some practice helps a lot before you go near a bushing your wanting to save, its messy and not hard to get off center and into the bushing and through it so fast, you don't have time to even say, OH SH*T.
We've done it for manure tanker spindles that are eight inch solid shafts and rusted tight, had to do my scraper steering cylinder pins to get the cylinders off so we could reseal them. Done quite a few walking tandems on wagons over the years and had to do the shafts on the front of my detaches like you just did, but mine was rusted solid and snapped off. We just cut the shafts off flush to the bushing and blew a hole through where the bushing was seized up at, took a hammer and knocked the remnants of the shaft out with a small hammer.
I also have the end with a gas valve and tab welded on separate and use a pipe coupler to hook a new three foot pipe to that I would call the consumable, that way I just put a new piece of pipe on when I'm done and its ready to go the next time and there is no welding or hooking up a gas valve again and nothing to remake for the next time. Hope this helps for next time, sorry I was too late to help you out on this project.