I have a very similar, almost identical machine in my mother's home and I use it when I stay there. It has a Celeron 400 CPU and 256 RAM and 32 GB hard disk. I've read that "The Intel Pentium III Processor had a clock speed range from 450 MHz to 1.4 Ghz" so under any condition you have a CPU faster than mine.
In the past I used Xubuntu on that machine. (Xubuntu is the official ubuntu release with Xfce desktop environment) I believe it can still handle it. (I haven't ever used Lubuntu so I can't comment on that.) The trick is: tandard installation CD of Ubuntu which serves as a live CD may be very slow because it is not installed on the machine and relies on the RAM to run. It doesn't give you an idea on the speed of the installed system. Especially on a machine with that much small RAM. Keep that in mind. You may even prefer to install from an "alternate CD"; which is an instalation CD with no live CD feature. (That's for Xubuntu; Debian CDs are not live CDs at all.)
Two weeks ago I installed Debian on that machine. (Ubuntu is very closely related with Debian, Ubuntu is a Debian based distribution.) Debian, as default, has much more less services working as default and in my opinion it is superior to Ubuntu for the task to learn GNU/Linux basics on an old machine.
I installed Debian 5.0.6 "stable" release from the iso CDs. (They have 5.0.7 at the moment so prefer that one.) I have no internet connection with that machine. So I created a CD from debian-506-i386-xfce+lxde-CD-1.iso This is the first installation CD of Debian containing Xfce and LXDE environments instead of Debian's default GNOME. The purpose is to be lighter, of course, and is suitable for old old machines.
At the beginning of the installation, you are given a choise to install Xfce or LXDE. Later you may install the other one you didn't opt in at the beginning as well. Rhen you'll have 2 desktop environments and choose one of them while logging in. I installed even GNOME desktop to my old machine and now I have 3 choises. (In fact more than 3; there's also a very plain X window system choise as I remember.) To install GNOME as well, you have to have the 1st CD (not the xfce+lxde one) as well.
Because I have no Internet connection, I created the first 5 CDs and I'm instaling packages from them. (There are 30+ CDs in total.)
As a result: Xfce (both Xubuntu and Debian versions) and LXDE (Debian one) and even GNOME (Debian) works well on the machine. So I see no reason that they won't work for you too.
About the performance: For sure, I installed GNOME just for some testing purposes. Xfce and LXDE are working like a charm on that machine. Starting od the services and applications are a little bit slow but when they start I even don't realize a slowness. That is to mean, machine starts a little bit slow. But when it starts there's no problem. Office package starts a little bit slow but once it starts there's no speed issue when writing... and so on. I have no problem with listening to the music on that system. I even can watch video but video performance is not that good. I don't advice to use [more than 2] relatively heavy programs at the same time.
For the command line, there's absoluıtely no problem. That kind of a machine is ideal to learn the basics of GNU/Linux.
I must admit that I like to work with that machine better than my "modern" laptop! I'm sure that your machine will host one of these choises and it will be a lovely GNU/Linux machine. Good luck.