Замените местоимение me другими местоимениями 1-го и 3-го лица. 1) let me have a look at the picture. 2) let me have a little rest.

1-го
1) Let us have a look at the picture.
2) Let us have a little rest.
3-го лица
1) Let him have a look at the picture.
2) Let him have a little rest.
1) Let her have a look at the picture.
2) Let her have a little rest.
2) Let it have a little rest.
1) Let them have a look at the picture.
2) Let them have a little rest.