Hi Mark.
Well. The replacement of entire numbered lines is basically as simple as can be with sed:
set filePath to "/Users/snaplash/Desktop/SNAPLASH_DO_NOT_DELETE/PROCESSING_DO_NOT_DELETE/" & listingMLSProviderPrefix of theRecord & Mlsid of theRecord & "_MARKER_20.html"
set replacementLine85 to "var address = '" & listingStreetNumber of theRecord & ", " & listingCity of theRecord & " " & listingState of theRecord & " " & listingZipcode of theRecord & "';"
set replacementLine122 to "icon: " & quote & "file://" & "/Users/snaplash/Desktop/SNAPLASH_DO_NOT_DELETE/CONSTANTS_DO_NOT_DELETE/LOGO_VAULT_DO_NOT_DELETE/" & brandingFolderName of theRecord & "/" & brandingFolderName of theRecord & "_EARTH_MARKER.png" & quote & ","
do shell script "sed '85 s|^.*$|" & replacementLine85 & "|
122 s|^.*$|" & replacementLine122 & "|' " & quoted form of filePath
The flies in the ointment when trying to replicate your TextWrangler script with sed are the possibilty of reserved sed characters in the replacement strings and the fact that writing back to the original file with sed leaves you with an empty file.
I’ve used vertical bars for the ‘s’ command delimiters above as there are several forward slashes in one of the replacement strings. If the strings contain ampersands, single-quotes (apostrophes), or backslashes, these need to be escaped. I hope there are no backslashes as they’ve totally defeated me for the moment. 
There are more convenient ways than sed to do this, but it’s Sunday. 
set filePath to "/Users/snaplash/Desktop/SNAPLASH_DO_NOT_DELETE/PROCESSING_DO_NOT_DELETE/" & listingMLSProviderPrefix of theRecord & Mlsid of theRecord & "_MARKER_20.html"
set replacementLine85 to "var address = '" & listingStreetNumber of theRecord & ", " & listingCity of theRecord & " " & listingState of theRecord & " " & listingZipcode of theRecord & "';"
set replacementLine122 to "icon: " & quote & "file://" & "/Users/snaplash/Desktop/SNAPLASH_DO_NOT_DELETE/CONSTANTS_DO_NOT_DELETE/LOGO_VAULT_DO_NOT_DELETE/" & brandingFolderName of theRecord & "/" & brandingFolderName of theRecord & "_EARTH_MARKER.png" & quote & ","
do shell script "# Join the two replacement lines with a linefeed, pass the quoted form of the result to sed to escape the linefeed and any ampersands or bars, and assign the result to a variable.
doctoredReplacements=$(sed -E '
# Insert a backslash at the end of the first replacement line to escape the linefeed and insert backslashes before any ampersands or bars in either line.
1 s/$/\\\\/
s/&|\\|/\\\\&/g' <<<" & quoted form of (replacementLine85 & linefeed & replacementLine122) & " );
# Read the file at filePath into sed to replace lines 85 and 122 with the doctored replacement lines. Assign the edited text to a variable.
editedText=$(sed '
# Replace line 85 with the block of two replacement lines, then delete the second.
85 {
s|^.*$|'\"$doctoredReplacements\"'|
s|\\n.*$||
}
# Replace line 122 with the block of two replacement lines, then delete the first.
122 {
s|^.*$|'\"$doctoredReplacements\"'|
s|^.*\\n||
}' " & quoted form of filePath & ") ;
# Retrieve the edited text from the variable and write the result back to the original file.
echo \"$editedText\" >" & quoted form of filePath
Edit: For comparison, the fast, simple, vanilla method would be:
set filePath to "/Users/snaplash/Desktop/SNAPLASH_DO_NOT_DELETE/PROCESSING_DO_NOT_DELETE/" & listingMLSProviderPrefix of theRecord & Mlsid of theRecord & "_MARKER_20.html"
set replacementLine85 to "var address = '" & listingStreetNumber of theRecord & ", " & listingCity of theRecord & " " & listingState of theRecord & " " & listingZipcode of theRecord & "';"
set replacementLine122 to "icon: " & quote & "file://" & "/Users/snaplash/Desktop/SNAPLASH_DO_NOT_DELETE/CONSTANTS_DO_NOT_DELETE/LOGO_VAULT_DO_NOT_DELETE/" & brandingFolderName of theRecord & "/" & brandingFolderName of theRecord & "_EARTH_MARKER.png" & quote & ","
set astid to AppleScript's text item delimiters
set fileAccess to (open for access POSIX file filePath with write permission)
try
set textLines to paragraphs of (read fileAccess as «class utf8»)
set item 85 of textLines to replacementLine85
set item 122 of textLines to replacementLine122
set AppleScript's text item delimiters to linefeed
set editedText to textLines as text
set AppleScript's text item delimiters to astid
set eof fileAccess to 0
write editedText to fileAccess as «class utf8»
close access fileAccess
on error errMsg
close access fileAccess
set AppleScript's text item delimiters to astid
display dialog errMsg buttons {"OK"} default button 1
end try