Again, what further innovations did these apps influence? Also, neither LHA/LZX or Rexx were Amiga "firsts." How about I say that Doom is one of the most influental Amiga apps?
Don't bust my balls, lol. We aren't ever going to come up with a master list of the best/most influential programs on the Amiga with 10 spaces to fill.
FYI, LZX was first on the Amiga. MS later snapped up Jonathan Forbes (of Xenolink BBS fame) and rolled the technology into the .cab format, among others. If you can't see where LZX ended up, well.... I really don't care if software was on a previous platform as long as it brought features when it was rolled onto the Amiga platform.
http://en.wikipedia.org/wiki/LZX_%28algorithm%29#Amiga_LZXWhile Arexx was not an Amiga first, anyone denying the impact it had on the Amiga OS and how Amiga programs interacted with each other via Arexx other is a fool. Further innovations? - it's still extremely useful in OS 4, I simply couldn't live without ARexx functionality on my SAM. ARexx was HUGE to the Amiga OS. Half the bloody apps like ADPro and the big guns in the AmigaOS SW area got a lot of life and power out of ARexx. Christ, I remember running a BBS on my old A4000 and running an ARexx script via said BBS to convert new uploaded images the minute they landed in ADPro, and fire them back to the user on the fly in another format. That was unheard of back then, the amount of give and take between programs. I ran an entire zone Fido subhub on a single A4000 with 4 Arexx scripts cause the RC couldn't do it on his 4 networked dosboxes cause they could not pull FTP'ed incoming echomail while tossing netmail packets.
Arexx was massive in regards to the professional market, and was absolutely instrumental in how the video/gfx/rendering appeal of the Amiga gained a foothold. Being able to swap data/files between programs via ARexx scripts/ports in the Toaster Suite with things like ADPro and other similar image processing stuff was a major selling point of the capabilities of the Amiga. If it wasn't an included feature of the program you bought, chances are said program had an ARexx port you could script for to allow program/file interaction, there were entire programs built on the back of an ARexx port. No serious Amiga program lacked an ARexx port.
if you want to pick nits - is Amiga Basic not a "first" or "native" app cause Microsoft coded it then ported it for C=?