In order to answer your query it would be best to start with a known individual whose Arms can be confirmed by sources other than the visitations, thus giving a firm foundation to work from. Can you give us a name and date, please ?
Sure and will also provide some of the sources, though I admit to making an error in my first post.
The one in the early 11th century was actually Llewelyn Aurdorchog, Lord of Ial (or Llewelyn ap Coel ap Gweirydd b. c1005) whose arms were
"azure, a lion rampant guardant or" These arms of Llewelyn Aurdorchog are listed in 'The general armory of England, Scotland, Ireland, and Wales' by Burke p613 as well as some of the below mentioned sources also A Display of Herauldry of the particular Coat Armours now is Use in the Six Counties of North-Wales by Reynolds, John p23.
The arms I mentioned in my OP are the direct descendant of the above Trahaearn ap Iorwerth Lord of Garthmael (b. c1170), given him by the Prince of Powys for his bravery in battle,
"argent, three lions passant in pale gules". This is mentioned in 'The history of the princes, the lords marcher, and the ancient nobility of Powys Fadog... by Jacob Youde William Lloyd, as well as some of the below mentioned sources.
https://archive.org/details/historyofprinces05lloy/page/120/mode/2upThe person I mention born around 1425 was Philip ap leuan (direct decent of the above) who married the heiress of Berthlwyd who's fathers arms were "
Ermine, a lion rampt. sable, in a border gules, charged with eight mullets or.". As seen in the above source of The history of the Princes... His arms are also given in some sources like the Archaeologia cambrensis as the same as his descendant Sir Edward Lloyd.
Philip's descendant was David Lloyd ap Jenkin (b. c1525) who was Mayor of Llanidloes and High Sherriff of Montgomeryshire. His arms were "
Quarterly 1 & 4, ermine, a lion rampant sable in a border gules charged with eight annulets ar.; 2 & 3, Party per bend sinister ermine and ermines, a lion rampant or." This according to "The sheriffs of Montgomeryshire, their armorial bearings and notices of their families, 1540 to 1639 by William Valentine Lloyd p228"
https://archive.org/details/sheriffsmontgom00lloygoog/page/n266/mode/2up as well as numerous other sources. This is similar to the Lloyds of Clochfaen arms in the general armory - Clochfaen being relatives to Berthlwyd family.
He had issue including 2 sons. One being Edward Lloyd (b. c1565) who's son was David Lloyd, Dean of St Asaph (b. 1597) of which the source in the OP shows his arms (though this is the only entry of it I have found and erroneously states his father as David Lloyd). "
Arms.: Gu., 3 boars' heads erased in pale arg. Lloyd. Crest.: Out of an heraldic coronet a boar's head erased arg. Motto.: Dare quam accipere." The arms it seems are listed in burkes armory attributed to the Lloyd family from denbigh.
https://archive.org/details/b22650611/page/270/mode/2upThe other son was Jenkin Lloyd who's son Sir Edward Lloyd married Ursula dau. of Sir Henry Salisbury. His arms and his descendants which became extinct around 1724 were "1st, argent, three lions passant in pale gules (Trahaiarn ap Iorwerth, lord of Garthmul); 2, ermine, a lion rampant sable in a border gules charged with eight bezants." giving credence to the afore mentioned arms. This is shown in Archaeologia cambrensis Vol.13 p260 about halfway down the page. This book also shows the previous mentioned arms as well.
https://archive.org/details/archaeologiacamb1867unse/page/260/mode/2upI also do understand that visitations cannot be trusted however this particular line does seem to be accurate through the male line based on the varied sources with the relevant corrections made. Additionally the Peniarth Manuscript's and Harleian Manuscript's (4181, 1973) the later of which has pedigrees and histories of the landholding families of Montgomeryshire confirm the lineage.
:EDIT:
Just an edit to this, there is also a desk that belonged to David Lloyd Dean of St Asaph that is shown in a catalogue of the library of John Holmes (1758-1841) which also has arms on it and the desk according to the date is from 1624. Whilst there are no heraldic colours shown, it does show the arms of the aforementioned Lord's of Ial as well as two others "
charged with three ducks" and another "
charged with three Pheons". The desk description can be found here:
https://archive.org/details/adescriptivecat02holmgoog/page/n282/mode/2up