The first searches for axions and axion-like particles with the Large Underground Xenon (LUX) experiment are presented. Under the assumption of an axio-electric interaction in xenon, the coupling constant between axions and electrons, gAe is tested, using data collected in 2013 with an exposure totalling 95 live-days $times$ 118 kg. A double-sided, profile likelihood ratio statistic test excludes gAe larger than 3.5 $times$ 10$^{-12}$ (90% C.L.) for solar axions. Assuming the DFSZ theoretical description, the upper limit in coupling corresponds to an upper limit on axion mass of 0.12 eV/c$^{2}$, while for the KSVZ description masses above 36.6 eV/c$^{2}$ are excluded. For galactic axion-like particles, values of gAe larger than 4.2 $times$ 10$^{-13}$ are excluded for particle masses in the range 1-16 keV/c$^{2}$. These are the most stringent constraints to date for these interactions.
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