We have used fibre spectroscopy to establish cluster membership and examine pre-main-sequence (PMS) lithium depletion for low-mass stars (spectral types F to M) in the sparse young (~30 Myr) cluster IC 4665. We present a filtered candidate list of 40 stars that should contain 75 per cent of single cluster members with V of 11.5 to 18 in the central square degree of the cluster. Whilst F- and G-type stars in IC 4665 have depleted little or no lithium, the K- and early M-type stars have depleted more Li than expected when compared with similar stars in other clusters of known age. An empirical age estimate based on Li-depletion among the late-type stars of IC 4665 would suggest it is older than 100 Myr. This disagrees entirely with ages determined either from the nuclear turn-off, from isochronal matches to low-mass stars or from the re-appearance of lithium previously found in much lower mass stars (the ``lithium depletion boundary). We suggest that other parameters besides age, perhaps composition or rotation, are very influential in determining the degree of PMS Li-depletion in stars with M greater than 0.5 Msun. Further work is required to identify and assess the effects of these additional parameters, particularly to probe conditions at the interface between the sub-photospheric convection zone and developing radiative core. Until then, PMS Li depletion in F- to early M-type stars cannot be confidently used as a precise age indicator in young clusters, kinematic groups or individual field stars.