Assuming this external hard drive has no special features that only Lion & above would have…hard to say.
Both Seagate and Western Digital have models of external hard drive that won't and *can't* be made to boot up a Macintosh. This has been a huge source of frustration for many Macintosh users. If you purchase one of these drives, have trouble with it, and call tech support, generally they will tell you that you are SOL. Western Digital external hard drives, in particular, are worth avoiding:
http://wdc.custhelp.com/app/answers/detail/a_id/1787
Note what it says on this page. Western Digital doesn't support Macintosh booting on *any* of their external hard drives. (Which isn't to say that you can't boot your Mac from a given WD external hard drive. It means that if you have any problem doing so, WD will be of no assistance whatsoever.)
Currently we are in a time when there are very few excellent external hard drives available, but quite a few poorly reliable ones. It's hard to know what to purchase.
Here is what I recommend:
If you want a reasonably priced and fairly reliable external hard drive drive, go with one from OWC:
http://eshop.macsales.com/shop/firewire/1394/USB/EliteAL/eSATA_FW800_FW400_USB
If you want the most reliable external hard drive drive you can purchase for not an insane price, you might find the slight premium for a Glyph Studio drive to be well worth it:
http://www.glyphtech.com/
http://www.glyphtech.com/products/studio
(Glyph drives aren't just well made. Glyph has outstanding service and support. They even offer data recovery as part of their warranty. A Glyph drive is built like a tank.)
Amazon offers Glyph drives at a discount:
http://is.gd/6rLM1d