The addition of sucrose to lysis buffer will increase osmotic pressure outside the cells that will help cell break.

Sucrose in lysis buffer will change osmolarity. There will be difference in osmolality between cytoplasm of cells in sucrose solution and outside the cell, hence sucrose will keep balance of osmolarity. Cell will swell and help in rupture process.

Glucose is also added in lysis buffer. Adding glucose to the buffer solution helps maintain osmolarity to keep the cells from bursting while adding

Would the result be the same (cell membrane lysis) if we used other sugars like xylose for example?

Also, is the nuclear membrane also broken in the process?

Thanks for the answer Muna and Ayshwarya.