NUMAH LITTERS OV KITTEHS ON TEH NETZ
Variable capitalization

IT IZ PRETTY GUD LOLCODE
HOWEVEZ ME THINKS THAT TEH LOLCODEZ R EZYR 2 READ IF TEH VARZ R lowercase
ZIS BECUZ ALL CAPS IS HARD TOO READ
(all spelling "mistakes" made by my cat, who assisted me in that part of this review)

More seriously, it is an issue that there are no good LOLCODE syntax highlighters. To be "stylish" and keep everything uppercase is a choice you can make, but personally I prefer to use lowercase or camelCase variable names whilst keeping the language constructs all caps. Similar to SQL, this allows you to see what parts of the code are variables, and what parts are language constructs.

Compare:

I HAS A NAUW ITZ A NUMBR
I HAS A LEZZ ITZ A NUMBR
IM IN YR LOOPZ NERFIN YR COWNTR TIL BOTH SAEM COWNTR AN DIFF OF 1 AN NUMAH
  NAUW R SUM OF NUMAH AN COWNTR
  LEZZ R DIFF OF NAUW AN 1
  VISIBLE SMOOSH NAUW AN " LITTERS OV KITTEHS ON TEH NETZ" MKAY
  VISIBLE SMOOSH NAUW AN " LITTERS OV KITTEHS" MKAY
  VISIBLE "WAN FALLS DOWN AN BREAKZ PAH"
  VISIBLE SMOOSH LEZZ AN " LITTERS OV KITTEHS ON TEH NETZ" MKAY
  VISIBLE ""
IM OUTTA YR LOOPZ


with...

I HAS A nauw ITZ A NUMBR
I HAS A lezz ITZ A NUMBR
IM IN YR LOOPZ NERFIN YR cowntr TIL BOTH SAEM cowntr AN DIFF OF 1 AN numah
  nauw R SUM OF numah AN cowntr 
  lezz R DIFF OF nauw AN 1
  VISIBLE SMOOSH nauw AN " LITTERS OV KITTEHS ON TEH NETZ" MKAY
  VISIBLE SMOOSH nauw AN " LITTERS OV KITTEHS" MKAY
  VISIBLE "WAN FALLS DOWN AN BREAKZ PAH"
  VISIBLE SMOOSH lezz AN " LITTERS OV KITTEHS ON TEH NETZ" MKAY
  VISIBLE ""
IM OUTTA YR LOOPZ


Variable naming

Regarding NUMAH, have you considered using NUMBAH? Similar meaning, but uses a more common mispronunciation.

Working around the spec

IM IN YR LOOPZ NERFIN YR COWNTR TIL BOTH SAEM COWNTR AN DIFF OF 1 AN NUMAH
  NAUW R SUM OF NUMAH AN COWNTR


This construct is non-obvious. You had to work around the spec to do something that you wanted to do, and I think it warrants explanation. Add a comment via BTW:

IM IN YR LOOPZ NERFIN YR COWNTR TIL BOTH SAEM COWNTR AN DIFF OF 1 AN NUMAH
  NAUW R SUM OF NUMAH AN COWNTR BTW workaround loop counters starting at 0


Correctness in corner cases

Your function doesn't check if the value passed in is greater than 0. This means that it falsely forces a KITTEH to break their paw when it wasn't necessary.

Add a guard clause at the top of the function; you can do an early return via GTFO.

DIFFRINT numbah AN BIGGR OF numbah AN 0
O RLY? YA RLY
    GTFO
OIC


Program definition

OBTW
    PRINT TEH LOLCODE VERSHUN OV N BOTTLEZ OV BER ON TEH WALL.
TLDR

HAI 1.3


Aside from the weird phrasing (does this code print the lolcode version of/and bottles of beer on the wall?), there's something else wrong here: Your comment is before the HAI 1.3. So any interpreter loading your file might not know what version you are using. Put your version number at the top. 

Possible alternative dialects

VISIBLE "NO MOAR LITTERs OV KITTEHS ON TEH NETZ"


Did you make a typo here, is this an alternative kitty dialect that uses lower case 's' for certain plurals? I'm not sure.



Lastly, I think this version of 99 LITTERS OV KITTEHS ON TEH NETZ is not authentic, as anyone knows that when KITTEHS fall, they'll be alright. This version is sad, as all the KITTEHS just break their paws. Proper LOLCODE uses cats, it doesn't abuse them.