The word "blithe" means carefree, light, indifferent, happy and care-free. People who are described as blithe are people who don't take things very seriously. They have a very "live and let live" attitude towards other people and towards life in general. They tend to wander through life instead of having serious plans and goals for themselves. They often do not consider the consequences of their actions; they're impulsive and and don't learn from their mistakes. They don't have much empathy for the feelings of others because they take so few things in life seriously. Thus, a person who is "blithely telling lies to people around him" is a person who knows that lying is wrong and unkind, but doesn't care all that much. He or she tells lies to others in a carefree manner without thinking of the consequences that these lies may bring.
If someone tells you a lie - that your best friend said you were ugly - and you believed it and this hurt your feelings badly, the person blithely told you a lie in a very uncaring, cheerful and carefree manner without thinking of how it hurt you.
If someone tells you a lie - that your best friend said you were ugly - and you believed it and this hurt your feelings badly, the person blithely told you a lie in a very uncaring, cheerful and carefree manner without thinking of how it hurt you.