First of all, don't coil your rope in the "usual" U-shape, like climbers do! (example picture)
Or in ASCII art
//// o \\\\
This form is good for carrying, but not for tossing.
You mention "lap-coiled", so probably you already know that, but it's worth mentioning (for the likes of me who used it many times with consistently poor results).
A better coiling form is "O-shaped", or spiral:
------------& (one end terminated by a knot)
When I coil my thin (8 mm) ropes, I place the coils in one hand, which is barely enough for 40 m of rope (I toss the rest separately) - any longer or thicker, and you would need to hold the coils in some other manner (on the arm or on the lap? Or maybe you have bigger hands than me? YMMV).
When making the individual coils, you should twist each one in such a way that it produces no kinks in the yet-uncoiled part of the rope. It's usually pretty easy - you do exactly the same 360° twist of the rope in each coil. All the coils should look as round and as identical as possible - it's fine if they look more like "D" than "O", but if they look like "8" - you are doing it wrong.
In addition (also important), try to place the coils into your hand in a consistent manner, so they could separate easily when tossed. Like this (your hand viewed from the side; "o" is the rope in cross-section):
| | |o | |o o | |o o o o | |o o o o o |
| | | o | | o o | | o o o o o| | o o o o o|
\o / \o o / \o o o / \o o o o / \o o o o /
\o / \o o / \o o o / \o o o / \o o o /
---- ---- ---- ---- ----
The final result is illustrated here, but please disregard the part about shaking off the kinks - if there are any kinks that you needed to shake off, the rope is unsuitable for tossing.