The pKa of tyrosine is 10.1 and the pKa of lysine is 10.5. At high pH, say >12, what is the protonation states of these species? Since pH > pKa for both of these cases, both will exist as the conjugate acids. Therefore, R-Ph-OH goes to R-Ph-O (1-) and Lys-NH3 (1+) goes to Lys-NH2. In other words, they both exist as their conjugate bases. Tyrosine becomes negatively charged and lysine loses charge. Thus, B is wrong.
Since the phenol in tyrosine is acidic, it loses a proton and thus gains a negative charge at high pH. This means that it will be strongly attracted to positive charges. Conversely, lysine is basic and thus it will lose a positive charge to become neutral at high pH. This means that it won't move towards any charge at all.