The difference between Lamentable and Sad

When used as adjectives, lamentable means causing sorrow, distress or regret, whereas sad means feeling sorrow.

check bellow for the other definitions of Lamentable and Sad

Lamentable as an adjective:

Causing sorrow, distress or regret; deplorable, pitiful or distressing.

Sad as an adjective:

Emotionally negative. Feeling sorrow; sorrowful, mournful. Appearing sorrowful. Causing sorrow; lamentable. Poor in quality, bad; shameful, deplorable; later, regrettable, poor. Of colours: dark, deep; later, sombre, dull.

Examples:

"She gets sad when he's away."

"The puppy had a sad little face."

"It's a sad fact that most rapes go unreported."

"That's the saddest-looking pickup truck I've ever seen."
Sad as an adjective (obsolete):

Sated, having had one's fill; satisfied, weary.
Sad as an adjective (obsolete):

Steadfast, valiant.
Sad as an adjective (obsolete):

Dignified, serious, grave.
Sad as an adjective (obsolete):

Naughty; troublesome; wicked.
Sad as an adjective (slang):

Unfashionable; socially inadequate or undesirable.

Examples:

"I can't believe you use drugs; you're so sad!"
Sad as an adjective (dialect):

Soggy (to refer to pastries).
Sad as an adjective (obsolete):

Heavy; weighty; ponderous; close; hard.

Examples:

"sad bread"