Is there a biophysical causation from local field potential (LFP) to spikes?
I am not sure that kind of action would be a "significant influence", but the general understanding is that LFP and spike frequency are inter-correlated (1, 2). An interesting recent publication on the topic (3), however, doubts this correlation as the nature of LFP recording and signal processing might introduce some artifacts to the recordings.

It would be interesting to see a correlation between the spike shapes and LFP, but I failed to find a relevant paper here.

References:


 Belitski A, Gretton A, Magri C, Murayama Y, Montemurro MA, Logothetis NK, Panzeri S. 2008. Low-frequency local field potentials and spikes in primary visual cortex convey independent visual information. The Journal of neuroscience : the official journal of the Society for Neuroscience 28: 5696–709.
 Rasch MJ, Gretton A, Murayama Y, Maass W, Logothetis NK. 2008. Inferring spike trains from local field potentials. Journal of neurophysiology 99: 1461–76.
 Zanos TP, Mineault PJ, Pack CC. 2011. Removal of spurious correlations between spikes and local field potentials. Journal of neurophysiology 105: 474–86.