One of the hardest things to achieve in LilyPond without a visual tool is tweaking slur positions. Using this tool you can generate the values for the appopriate override. Clicking this button will display one blue handle and four black handles and a dialog box. Position the blue handle to the middle line, horizontally aligned to the left of the notehead, where the slur begins, then use the black handles to create the expected shape of the slur like this:

Figure 5.1. The Slur Tweak Tool

As you can see in the picture you might want to use a big zoom to set the slur. Pressing the Write to clipboard button will write the appropriate \override to the clipboard, which you can paste into the document. In this example, the generated text is \override Slur #'control-points = #'( ( 2.6265 . 2.535) ( 5.5247 . 3.985) ( 8.8758 . 3.985) ( 11.683 . 2.988) ), and will result in the following image:

Figure 5.2. Result of slur tweak