It's weird. Maybe it's a typo or something.
As far as I know, t wouldn't lenite after the article in Old Irish, nor in Modern Irish... why would it lenite in Classical Irish?

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

The grammatical texts permitted it, why they did I don't know. They explicitly ignored the dentals rule in general, I'll get the reference.

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The dialect I use is Cork Irish.
Ar sgáth a chéile a mhairid na daoine, lag agus láidir, uasal is íseal

I've found what apparently is an older version -

Go mbeannaithir duit a Mhuire
atá lán de ghrásta
tá an Tighearna id h-ochair
is beannaithe thú idir mná
agus is beannaithe toradh ded'bhroine Íosa
A Naomh-Mhuire, a Mháthair Dé
guigh orainn na peacaigh
aníos, agus ar uair ár mbáis
Áiméan

I haven't seen 'id h-ochair' before and is 'ded'bhroine' correct?

In classical Irish in 'An Thighearna' was the dental fricative enunciated or was it just t and written 'th'?

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