Great question.
Do understand that presbyopia occurs as a result of age-related changes in the lens of the eye.
LASIK or any forms of laser vision correction (LVC) makes its effect felt by way of changes on the surface of the eye, namely the cornea. Hence, LVC cannot spare patients from the inevitable effects of presbyopia that effects everyone in their middle ages.
It is possible though to correct your residual myopia and astigmatism. This would allow you to have good unaided vision at far distances but you would still need to rely on reading glasses for the close distance.
In some cases, the surgeon may leave one eye slightly myopic to enable you to read through that eye without glasses. This is called monovision. Discuss this with your surgeon and he may offer you a trial of monovision with the use of contact lens.