Yes it can, except …
Solution chemistry is really exchange reactions. In order to protonate any pair of electrons, you will need an acid that can coordinate the a pair of electrons more strongly than to another group. The effect of adding a proton to a nucleus is to increase the Coulombic attraction and pull the electrons in. The acidity follows HF>H
2O>NH
3>CH
4. Adding a proton to a compound also increases the effective nuclear attraction for the electrons. Therefore H
3O
+ is a stronger acid than H2O which is stronger than HO
-. For HO
-, it is the opposite effect. Removing a proton, decreases the effective nuclear attraction for its electrons. The electrons extend further and they are more available to react.
If you protonate the electrons of water, the remaining electrons will be pulled nearer to the nucleus. It will be harder to protonate them. If you were to protonate hydronium ion, you would need a compound in which the electrons of the conjugate base were more resistant to protonation than H
3O
+. I am not aware of any common reagents that can do this, so hypothetically you can protonate the lone pair, but practically you cannot.
You may be interesting in reading about the effect of atomic charge on electron availability here:
http://orgo.curvedarrow.com/punbb/viewtopic.php?id=347