Lagrangian coherent structures (LCS) are separatrices revealing the dynamics of a fluid flow, such as vortices, stagnation and separation/attachment lines and surfaces. Attracting and repelling LCS may be inferred from the finite-time Lyapunov exponent (FTLE), a measure of the maximum growth rate of the distance between two initially close fluid particles over a finite time interval. However, even from exact velocity fields, separatrices are difficult to accurately identify unless using fine grids. Anisotropic mesh adaptation has shown to be an accurate and computationally efficient alternative to cartesian grids, stretching mesh elements along the LCS and offering better ridges resolution for a given number of degrees of freedom. Here, we extend this methodology in 2D to anisotropic isoparametric $P^2$ triangles and describe a framework for the generation of curvilinear triangle meshes adapted to the curved features of LCS. Our method is applied to LCS extraction by computing FTLE ridges from both analytical and experimental velocity fields.