What would happen if a plane lost half of its weight instantly?
In steady flight, the lift $L$ generated by the wings equals the loaded weight so that there is no vertical acceleration.  Thus, the lift just before the bomb is dropped is
$$
L = m_1g =  245\,250 \;\textrm{N}
$$
where  $m_1=25\,000$ kg is the loaded mass and $g=9.81$ m/s$^2$ is the acceleration due to gravity.

In the time interval just after the $10\,000$ kg bomb is dropped, the lift remains the same until the lift is reduced to again balance the new mass of $m_2=15\,000$ kg. During that transient period, the Lancaster will accelerate upwards at
$$
a = \frac{L-m_2g}{m_2} = \left(\frac{m_1-m_2}{m_2}\right)g
$$
which works out as an upward acceleration of two-thirds of a "gee":
$$
\frac{a}{g} = \frac{m_1-m_2}{m_2} = \frac{2}{3}
$$

As @sanchises pointed out, the steady increase in the upward velocity results in a decrease in the angle of attack, so that the aircraft will again settle in a steady climb.