100% legal.
Easy launch on town Beach (left of slip) IF WEATHER IS GOOD! .....on hard sand most of the way.
You can drive up and dump the Boat,but will have to then park up before launching.I suggest you get there EARLY! Lyme in the summer is a Ball ache for parking..
Don't know the size of your party,but it's a lot easier with more hands.
Otherwise pay your fees and use the slip and Harbour...You MAY be able do a deal with the Harbourmaster to use the pontoons,which are there all summer or if your really lucky a mooring
Keep off Monmouth Beach to the West as its more exposed and steeper,longer to walk....and over big pebbles.
Charmouth and Seatown are worth a look too
Weather and a good forecast is the main thing...but you have the Harbour/slip as a fallback option.
Launching from Lyme also entitles you to use the Harbour and facilities at Westbay...never been asked for proof
but much better Food and Pubs!