Answer
A Lewis base is an electron pair donor. Water has one active lone pair that can do so (forget about having four-coordinate oxygen).
In this reaction, water is the Lewis base, H+ is the Lewis acid(notNH+4) Water donates the electron pair, and the H+ on NH+4accepts that electron pair to make a bond.
NH+4is then a Brønsted-Lowry acid, being a proton donor, and water is then also the Brønsted-Lowry base, being a proton acceptor.
The way I drew hydronium is a bit misleading. What is the actual molecular geometry of hydronium?