Do you know if it's possible to use a "standard" programming tool, such as the USBtinyISP or AVRISP to upload code to this device?
Don't think so. Even Atmel's flagship programmer 'Atmel ICE' does not have support for at89lp. I have only read about David Prentice having built a modified usbasp firmware with at89lp support. I did not find the sources though.
With a little effort I think it's possible to add Arduino support for this family!
I don't think that is worth the effort, though that is subjective: you might have a personal motivation to do so... But not many people have this hardware and it is not a new platform that is about to boom like all these Arm cortex mcu's. I think Atmel carries these chips for companies with 8051 based designs they don't want to modify or that want to continue with 8051 for some reason...
That said, I did some experiments, e.g. an equivalent of Arduino's tone api. I think I 'll add them as samples to the blog post. Maybe there are still a few people interested in the at89lp and it might help them get it up and running.