There is a ticket for the support of dialectal Arabic variants more generally (T187344), however, it does not explicitly concern lexemes, and there are a number of codes which would be useful for lexicographical data which may not necessarily see much use in other contexts. I have assembled a list with English names; I can add and provide additional context or justification for any or all of these if requested.
aao - Algerian Saharan Arabic
abh - Tajiki Arabic
abh-af - Balkh Arabic
abh-tj - Bukhara Arabic
abv - Bahrani Arabic
acm-ir - Khuzestani Arabic
acq - Taʽizzi-Adeni Arabic
acq-u-sd-yela - Tihami Arabic
acw - Hejazi Arabic
acw-u-sd-sa14 - Beqari Arabic
acx - Omani Arabic
acy - Cypriot Maronite Arabic
acy-arab - Cypriot Maronite Arabic (Arabic script)
acy-grek - Cypriot Maronite Arabic (Greek script)
acy-latn - Cypriot Maronite Arabic (Latin script)
adf - Dhofari Arabic
aeb-hebr - Judeo-Tunisian Arabic
afb - Gulf Arabic
afb-ae - Emirati Arabic
afb-bh - Bahraini Arabic
afb-kw - Kuwaiti Arabic
aju - Judeo-Moroccan Arabic
apc-jo - Jordanian Arabic
apc-lb - Lebanese Arabic
apc-ps - Palestinian Arabic
apc-sy - Syrian Arabic
apc-tr - Cilician Arabic
apd - Sudanese Arabic
ar-az - Shirvani Arabic
ar-ye - Yemeni Arabic
arq-hebr - Judeo-Algerian Arabic
arz-hebr - Judeo-Egyptian Arabic
auz - Uzbeki Arabic
auz-ir - Khorasan Arabic
auz-uz - Qashqa-Darya Arabic
avl - Northwest Arabian Arabic
ayh - Hadhrami Arabic
ayh-id - Indonesian Arabic
ayl - Libyan Arabic
ayl-eg - Western Egyptian Bedawi Arabic
ayn - Sanʽani Arabic
ayp - North Mesopotamian Arabic
ayp-tr - Anatolian Arabic
jye - Judeo-Yemeni Arabic
kcn - Nubi
mey-arab - Hassaniya Arabic (Arabic script) (Mauritania)
mey-latn - Hassaniya Arabic (Latin script) (Senegal)
mt-arab - Maltese (Arabic script)
pga - Juba Arabic
pga-arab - Juba Arabic (Arabic script)
pga-latn - Juba Arabic (Latin script)
shu-cm - Cameroonian Arabic
shu-latn - Chadian Arabic (Latin script)
shu-ng - Nigerian Arabic
sqr - Siculo-Arabic
ssh - Shihhi Arabic
xaa - Andalusian Arabic
yhd - Judeo-Iraqi Arabic
yud - Judeo-Tropolitanian Arabic