From OMIM
Li-Fraumeni syndrome (LFS) is a clinically and genetically heterogeneous inherited cancer syndrome. LFS is characterized by autosomal dominant inheritance and early onset of tumors, multiple tumors within an individual, and multiple affected family members. In contrast to other inherited cancer syndromes, which are predominantly characterized by site-specific cancers, LFS presents with a variety of tumor types. The most common types are soft tissue sarcomas and osteosarcomas, breast cancer, brain tumors, leukemia, and adrenocortical carcinoma. Classic LFS is defined as a proband with a sarcoma before the age of 45 years and a first-degree relative with any cancer before the age of 45 years and 1 additional first- or second-degree relative in the same lineage with any cancer before the age of 45 years or a sarcoma at any age (Li et al., 1988). Li-Fraumeni-like syndrome (LFL) is defined as a proband with any childhood cancer, or a sarcoma, brain tumor, or adrenocortical tumor before the age of 45 years, plus a first- or second-degree relative in the same lineage with a typical LFS tumor at any age, and an additional first- or second-degree relative in the same lineage with any cancer before the age of 60 years (Birch et al., 1994). A less restrictive definition of LFL is 2 different LFS-related tumors in first- or second-degree relatives at any age (Eeles, 1995). Approximately 70% of LFS cases and 40% of LFL cases contain germline mutations in the p53 gene on chromosome 17p13.1 (Bachinski et al., 2005).  http://www.omim.org/entry/151623

From MedlinePlus Genetics
Li-Fraumeni syndrome is a rare disorder that greatly increases the risk of developing several types of cancer, particularly in children and young adults.

The cancers most often associated with Li-Fraumeni syndrome include breast cancer, a form of bone cancer called osteosarcoma, and cancers of soft tissues (such as muscle) called soft tissue sarcomas. Other cancers commonly seen in this syndrome include brain tumors, cancers of blood-forming tissues (leukemias), and a cancer called adrenocortical carcinoma that affects the outer layer of the adrenal glands (small hormone-producing glands on top of each kidney). Several other types of cancer also occur more frequently in people with Li-Fraumeni syndrome.

A very similar condition called Li-Fraumeni-like syndrome shares many of the features of classic Li-Fraumeni syndrome. Both conditions significantly increase the chances of developing multiple cancers beginning in childhood; however, the pattern of specific cancers seen in affected family members is different.  https://medlineplus.gov/genetics/condition/li-fraumeni-syndrome