Yes, the edible part of a lychee fruit is soft and pulpy.
Lychee fruit consists of a rough, inedible outer skin and a juicy, translucent white flesh (aril) inside. This flesh is what's eaten, and it has a soft, slightly chewy, and pulpy texture. The taste is sweet and mildly aromatic, making it a popular dessert fruit. Think of the texture as similar to a grape, but with a slightly firmer bite.
In summary, while the outer skin is hard, the inside of a lychee is indeed soft.
