Plot with different x-axis and y-axis using matplotlib

First, your data is string. You should convert them into floats.

Then, the easiest way to do is to call plot function multiple times, one for each line:

x =  [['12.63', '13.50', '14.15', '15.18', '16.04', '17.28', '18.56', '19.70',
       '20.90', '22.21', '23.25', '24.13'],
      ['13.39', '14.10', '15.05', '16.20', '17.55', '18.43', '19.75', '21.29',
       '22.78', '24.00', '24.85', '24.81'],
      ['13.02', '13.86', '14.82', '15.80', '16.90', '17.99', '19.24', '20.79',
       '22.30', '23.43', '24.38', '24.68']]

y = [['-15.09', '-15.19', '-15.23', '-15.32', '-15.07', '-15.11', '-15.04',
      '-15.08', '-14.97', '-14.98', '-14.89', '-15.12'],
     ['-15.91', '-15.89', '-15.90', '-15.96', '-15.55', '-15.58', '-15.51',
      '-15.48', '-15.42', '-15.40', '-15.85', '-16.64'],
     ['-15.71', '-15.75', '-15.83', '-15.83', '-15.54', '-15.55', '-15.53',
      '-15.47', '-15.41', '-15.33', '-15.43', '-15.97']]

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
ax.plot([float(n) for n in x[0]], [float(n) for n in y[0]], color='tab:blue')
ax.plot([float(n) for n in x[1]], [float(n) for n in y[1]], color='tab:orange')
ax.plot([float(n) for n in x[2]], [float(n) for n in y[2]], color='tab:red')
plt.show()