Albert Barnes Commentary Psalms 78:36

"But they flattered him with their mouth, And lied unto him with their tongue." — Psalms 78:36 (ASV)

Nevertheless they did flatter him with their mouth - The word rendered “flatter” properly means “to open.” Hence, it can mean “to be open, to be ingenious or frank,” and then, “to be easily persuaded, to be deluded, to be beguiled.” In an active form, it also means to persuade, to entice, to seduce, to beguile, or to delude.

The meaning here is that they attempted to deceive by their professions, or that their professions were false and hollow.

Those professions were the mere result of affliction. They were based on no principle; there was no true love or confidence at the foundation. Such professions or promises are often made in affliction. Under the pressure of heavy judgments, the loss of property, the loss of friends, or the failure of health, people become serious and resolve to give attention to religion.

It is rare that such purposes are founded in sincerity, and that the conversions apparently resulting from them are true conversions. The Septuagint and the Latin Vulgate render the phrase here, “They loved with their mouth.”

And they lied to him with their tongues - They made promises which they did not keep.