from small-scale physics can also be included using techniques inspired by effective field theory theory [@Vlah:2015sea; @Vlah:2016bcl]. In the context of MG cosmologies, extensive studies have been performed in the framework of Eulerian Standard Perturbation Theory (SPT) [@PhysRevD.79.123512; @Taruya:2013quf; @PhysRevD.88.023527; @PhysRevD.90.123515; @PhysRevD.92.063522; @Fasiello:2017bot; @Bose:2017dtl; @Bose:2018zpk]. LPT was first found to work very well within the COLA hybrid framework for chameleon and Vainshtein MG cosmologies [@Valogiannis:2016ane], while third order LPT for dark matter was recently developed in the case of scalar-tensor theories in [@Aviles:2017aor].

In this work, we perform a comprehensive study of how LPT can be used to make predictions for biased tracers in modified gravity theories, and how well the predictions compare with full numerical simulations for a variety of modified gravity models. We study chameleon and Vainsthein MG theories, focusing on the $f(R)$ Hu-Sawicki [@Hu:2007nk] and $n$DGP braneworld models [@Dvali:2000hr] as popular, representative examples for each category. The underlying dark matter clustering is described using the formalism in [@Aviles:2017aor]. We then consider the Convolution Lagrangian Perturbation Theory (CLPT) [@2013MNRAS.429.1674C] for biased tracers, as well as the variants, using the particular resummation scheme in [@Vlah:2015sea; @Vlah:2016bcl]. We extend the peak-background split formalism (PBS) [@1984ApJ...284L...9K; @1986ApJ...304...15B; @PhysRevD.88.023515] in which the 