The difference between small-signal and large-signal models of devices, components, etc.., is precisely that large signal models are intended to fully describe the nonlinear characteristics of the device, component, etc.. independently of the amplitude of the input signal(s), whereas small signal models are linear models which are extracted by linearization, i.e. by performing a first-order Taylor series expansion of the nonlinear characteristic of a device, component, etc... in correspondence of one specific operating point. As such, small-signal models are linear, are valid only for small variations of the input signals close to the operating point and do not describe non-linear effects/phenomena at all (as a matter of fact, the small signal model is linear). Nonetheless, the approach used in the derivation of small signal models can be extended (e.g. performing higher order Taylor series or Volterra series expansions of the nonlinear characteristics) so that to include a polynomial description of the nonlinearity. This last approach is probably the more convenient to analyse/design the effects of nonlinearity in a circuit/system intended to be linear, as a CMOS LNA and to estimate related parameters (HD2,HD3,IP3, etc..), since full large-signal models are often rather complex and impractical for pen-and-paper analysis and design, whereas they could be conveniently used in simulations. Unlike true large-signal models, even polynomial models are only valid for relatively small variations (larger than linearized models) of the input signal with respect to a bias point and can be therefore regarded, broadly speaking, as "small-signal models".

Definitely, you have to use large signal model. You cannot investigate linearization techniques using small signal model, because then there is no effect to linearize. I suggest trying it first in an analysis program. Then you have to specify the large signal properties of the investigated LNA, such as IP3, P1dB. You can use catalog data.

we developed a high gain pre-distortion linearizer for TWT( paper is available here). For its analysis we used large signal parameters in ADS. 

LNA is used as a front end amplifier in receiver and it deals with small signal as it has to handle a small signal. In case of  specific application where large signal is an input and still you need low noise amplifier (I am not able to imagine such requirement), analysis can be carried out

Nonlinear distortion of components intended to be linear is a major concern, especially for an LNA which is at the first stage of a receiver. Distortion can be related not only to the amplitude of the nominal signal, but also to out-of-band interferers whose power can be larger than the intended signal and which are not sufficiently rejected by filtering.

Nonlinear effects are not highlighted by so-called "small signal" models, hence nonlinear analysis, to be performed using either polynomial or "large signal" models is needed to highlight distortion (HD2,HD3,IP3, etc..) and is of great importance.