There are many reasons why people have cracked lips or at the side corner of their mouth.
Most likely, one have a mineral and vitamin deficiency in iron, vitamins A, B, and C respectively. Crack lips is also caused due to exposure to the wind, cold or dry air.
Or it maybe a sign of a fungal infection such as thrush, which also causes redness around cracks. It maybe due to allergy or slight allergic reaction to an ingredient in a cosmetic product one has recently started using.
To avoid cracks on lips, keep it hydrated by applying a thick unscented ointment like petroleum jelly. If it is caused by any of your new cosmetics, stop for a while, then slowly introduce them one at a time.
If the cracks persist , worsen or seemed infected consult a doctor if its about your diet or be tested and treated for any allergic reaction or fungal infection.