This is a scan of page 145 of the Jaiminiiya-prayoga-vivaraNa by A. Rangasvaami Ayyangaar, printed in grantha and Tamil scripts at Kumbhakonam in 1923. Here you see a Jaiminiiya Saamaveda saaman printed in grantha. The entire text on this page is in Sanskrit and grantha, but because in the Jaiminiiya branch of Saamaveda surviving only in South India, the Sanskrit word iDaa is rendered iZaa, it is necessary to use the corresponding Tamil-Malayalam letter ழ to express this. You see it in the middle of the third line from the bottom on this page - Asko Parpola, University of Helsinki.
This is the east coast variety of Grantha script. In west coast variety, the letter LLLA and is Chillu LLL is extensively employed.
[will add pictures]
See Grantha script as applied to a Dravidian language (Malayalam):
Alphabetum grandonico-malabaricum sive samscrudonicum.
Clemente, di Gesù (1731-1782); Giovanni Cristoforo Amaduzzi(1740-1792),
1772, Latin Book xxviii, 100 p. viii fold. pl. 19 cm.
Publication: Romae, typis Sac. congregationis de propag. fide,
Tamil is written in Grantha script (1289 CE) onwards:
" Curiously enough we find a copper-plate grant containing an inscription
having Sanskrit and Tamil sections both written in the Grantha script .
The date of the record falls in 1289 AD. The Tamil portion is entirely
transliterated in Grantha script following only the written form and
*not*the form of pronunciation
 Ep. Ind., XXXVII, pp. 175 ff