Note that it's not possible to reach Blue Lagoon from the south, unless you're arriving by boat in the floods!
Blue Lagoon is reasonably well signposted, and there are several ways to reach it. From Lusaka, the easiest is probably to take the great west road towards Mumbwa then turn left after about 22km, opposite the farmer's filling station. This all-weather gravel road will lead you to the national park's scout camp at Naleeza. Alternatively, if you're heading for Nakeenda Lodge then follow the sign left, and you can sign in there.
From the west
If coming from the west, pass through Mumbwa and look for a Total garage near Nangoma, around 81km east of Kafue's Nalusanga Gate. Fill up here. Then continue towards Lusaka for a few hundred metres, taking the first right turn after this filling station, following the power lines. In less than a kilometre, turn right at the crossroads and keep following those power lines! This junction is on a local bus route, so if you ask directions you will probably end up with a guide and their luggage. (A fair deal all round!) Continuing for 9km brings you to Myooye village, where you should take the left fork that passes the clinic on the right-hand side.
Follow this track for 31km to a T-junction, ignoring smaller side-tracks. (If the group of huts on the left, halfway along this road, has a flag flying, it means that the Tonga chief who lives here is in residence.) At this T-junction turn right. To reach Nakeenda Lodge, continue straight on for about 10km then turn left at the signpost, and sign in with the scout at the lodge.
If you're not going to Nakeenda, then turn right at the T-junction, and continue for 22km, ignoring a right-hand turn, passing through the first gate and finally reaching the scout post. At the post, sign in, pay the park and camping fees, and check the current camping rules with the scouts. You may end up turning around to retrace your tracks for 11km, before passing through the gate and turning right at the road signposted to 'Nakeenda Wildlife Police Unit'. This road quickly passes a derelict entry and after 7km reaches Nakeenda Lodge.