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In general, any lattice embedding $i\\colon \\mathbb{L} \\longrightarrow \\mathbb{M}$ between two lattices $\\mathbb{L} \\subseteq \\mathbb{M}$ induces a Banach lattice homomorphism $\\hat \\imath\\colon FBL \\langle \\mathbb{L} \\rangle \\longrightarrow FBL \\langle \\mathbb{M}\\rangle$ between the corresponding free Banach lattices. We show that this mapping $\\hat \\imath$ might not be an isometric embedding neither an isomorphic embedding. 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