As you change course, you must comply with rule 16:
"When a right-of-way boat changes course, she shall give the other boat room to keep clear."
The definition of "Room."
"The space a boat needs in the existing conditions, including space to comply with her obligations under the rules of Part 2 and rule 31, while manoeuvring promptly in a seamanlike way."

"existing conditions" is defined somewhat in case 134:
"A boat’s proper course at any moment depends on the existing conditions. Some of those conditions are the wind strength and direction, the pattern of gusts and lulls in the wind, the waves, the current, and the physical characteristics of the boat’s hull and equipment, including the sails she is using."

Though it may seem as though this puts some limit on L to accommodate W's more limited ability to come up, the rest of the case actually favors you. In this case, a boat rounding a windward mark notices the boat in front of her is having troubles with her spinnaker set. The trailing boat elects to delay setting hers, gets an overlap to leeward from clear astern. She than sails higher (proper course for her current sails). Windward protested Leeward saying that her proper course should have set her spinnaker and sail lower to the next mark. The appeals committee decided that there was no rule that said leeward had to set her spinnaker and therefore could sail the proper course for the sails she had at the time.

So, my conclusion is that you might have to luff slower to give W a bit more room, but can come up and the windward boat has to respond. You do not need to give her room to take her sails down. If she cannot get clear, she breaks rule 11. 

I'm assuming this is a fleet race, not a match race, but match racing call G2 might be useful. I'll leave it to the actual rules experts here to weigh in on whether G2 is applicable in a fleet race.

https://www.racingrulesofsailing.org/cases/835

Question 1
Blue is sailing to leeward of Yellow. Both boats have spinnakers set. Blue luffs Yellow. What are the obligations on Blue and Yellow?
Answer 1
Yellow is required to keep clear and Blue is required to give Yellow room to respond to her luff. While Yellow is able to keep the majority of her spinnaker filled and drawing she is not entitled to additional room to drop her spinnaker.
If Blue continues her luff so that Yellow, in order to keep clear, has to luff beyond the point where she can keep her spinnaker filled and drawing, then Blue must give Yellow room to drop her spinnaker.
Whether or not Yellow drops her spinnaker at that time, she is still required to keep clear. If she does not drop her spinnaker at that time, then Blue is not required to give her additional room to drop the spinnaker later in that luff.

Question 2
If Yellow does not drop her spinnaker and passes head to wind to keep clear, is Blue giving Yellow room to keep clear in a seamanlike way?
Answer 2
Yes. Blue may continue to luff as long as she has previously given Yellow room to drop her spinnaker.

Question 3
Does either answer change if Blue does not have a spinnaker set, or if Blue has a different type of spinnaker set?
Answer 3
No.

I see nothing inconsistent in the fleet rules and match racing rules that would proclude that example.  The situation would include the level of participants (match racing experts vs beer can) on what would be considered enough room to react as well as sea state, wind and boat type.  Has anyone searched thr casebook to see if there is an interpretation comparable to the callbook?