I don't know if you count it as an old phone but I use it on a Samsung SIII (Wikipedia says that launched 2012) and it's snappy as heck.
The current images are nightlies so I have encountered a few bugs. Previously was running CyanogenMod 13 on a stable image and that was fine (but the CyanogenMod company folded so it wasn't going to get security updates). Looking forward to a stable release of Lineage.
~I don't think Lineage OS 13 exists.~ (edit: it seems it does for some models). CyanogenMod 13 was Android 6 I believe and Lineage 14 nightlies are currently 7.1.2.
It exists. But I guess I get why you might be thinking this: with CM13 there were nightly builds for lots and lots of devices, but with LOS13 they heavily reduced the amount of devices for which they build nightlies.
I'm not sure if this means that they ceased to support LOS13 for these devices entirely. But it does seem that way, on account of how long it's been since the device tree ('DT') and kernel for my phone have seen any update. (HTC One M9, a.k.a. himaul)
Nowadays I just build LOS13 myself every once in a while, because it still receives generic updates and fixes, and luckily the current kernel and DT still work fine. It's just that, while the DT also wasn't updated that often back on CM13, iirc the kernel did receive updates and fixes fairly regularly. With that no longer being the case is why I suspect they halted supporting it at all.
My reason for staying on LOS13 rather than to upgrade to LOS14 is that the Xposed Framework does not exist for LOS14 / Android N. So that's what I'm waiting for. I wish the LOS13 would recognize how many people want to use 13 on the M9 and provide updates even if it's just once a month. Or maybe they do recognise this, but they just don't have the manpower, resources, or heck maybe there were too many problems when users switched from CM to LOS... I don't know.
There is just one really annoying error which I don't know how to fix, which is that the default camera app crashes, I suspect because of face detection. I thought they fixed that on CM13 ages ago. I guess he bug snuck back in. The OpenCamera does not crash, thank heavens, but it's still a nasty issue I wish would be addressed.
Anyway. My point was that it's still possible to build LOS13 for many devices.
The current images are nightlies so I have encountered a few bugs. Previously was running CyanogenMod 13 on a stable image and that was fine (but the CyanogenMod company folded so it wasn't going to get security updates). Looking forward to a stable release of Lineage.