One thing about using lipofectamine 2000 is that, the culture needs to be >85% confluence, or else it tends to kill cells quickly. Thus, I suggest you to start with a bit higher cell density. HEK293 is really easy to transfect once you catch the right condition. As I am not sure the size of your culture dish, please double check the amount of DNA per size on the instruction sheet to make sure that your DNA amount is within the range of the company's suggestion. Having too much DNA will also kill the cells (I learnt it the hard way).
I do notice that HEK293 cells won't attach tightly to the culture dish comparing to other cell types... The only trick that I have is to avoid adding media directly on top of the cells. Instead, gently add the liquid from the side wall. This should help to minimize cell loss...