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A growing disquiet has emerged in recent years that standard stellar modelsare at odds with observations of the colour-magnitude diagrams (CMDs) andlithium depletion patterns of pre main sequence (PMS) stars in clusters. Inthis work we select 1,246 high probability K/M-type constituent members of 5young open clusters (5--125\,Myr) in the Gaia-ESO Survey to test a series ofmodels that use standard input physics and others that incorporate surfacemagnetic fields or cool starspots. We find that: standard models providesystematically under-luminous isochrones for low-mass stars in the CMD and failto predict Li-depletion of the right strength at the right colour; magneticmodels provide better CMD fits with isochrones that are $\sim 1.5-2$ timesolder, and provide better matches to Li depletion patterns. We investigate howrotation periods, most of which are determined here for the first time fromTransiting Exoplanet Survey Satellite data, correlate with CMD position and Li.Among the K-stars in the older clusters we find the brightest and leastLi-depleted are the fastest rotators, demonstrating the classic "Li-rotationconnection" for the first time at $\sim 35$ Myr in NGC 2547, and finding someevidence that it exists in the early M-stars of NGC 2264 at $<10\,$Myr.However, the wide dispersion in Li depletion observed in fully-convectiveM-dwarfs in the $\gamma$ Vel cluster at $\sim 20$ Myr appears not to becorrelated with rotation and is challenging to explain without a very large($>10$ Myr) age spread.

The Gaia-ESO Survey: Constraining evolutionary models and ages for young low mass stars with measurements of lithium depletion and rotation