To solve this problem, we need to analyze the structure and bonding of diamond and graphite.$\\$• Diamond and graphite are both allotropes of carbon, meaning they are different structural forms of the same element.$\\$• In diamond, each carbon atom is $sp^3$ hybridized, forming a three-dimensional network. Each carbon atom is covalently bonded to four other carbon atoms in a tetrahedral geometry.$\\$• In graphite, each carbon atom is $sp^2$ hybridized, forming a two-dimensional planar structure. Each carbon atom is covalently bonded to three other carbon atoms in a trigonal planar geometry, with delocalized electrons allowing for electrical conductivity.$\\$Now, let's evaluate each option:$\\$Option 1: Diamond and graphite have two-dimensional network structures.$\\$• This is incorrect. Diamond has a three-dimensional network structure, while graphite has a two-dimensional planar structure.$\\$Option 2: Diamond is covalent, and graphite is ionic.$\\$• This is incorrect. Both diamond and graphite are covalent structures. Graphite has delocalized electrons, but it is not ionic.$\\$Option 3: Diamond is $sp^3$ hybridized, and graphite is $sp^2$ hybridized.$\\$• This is correct. Diamond is $sp^3$ hybridized, and graphite is $sp^2$ hybridized.$\\$Option 4: Both diamond and graphite are used as dry lubricants.$\\$• This is incorrect. Graphite is used as a dry lubricant due to its layered structure, but diamond is not used as a lubricant.$\\$Therefore, the correct statement is Option 3.