I was thinking about this recently and recognized that you do get free dodges. If you dodge a queue and lose 3 or 10 LP, then unless you’re left with so much less LP that you would need another win to reach 100, the dodge was free. Here’s an example from my recent experience:
Sitting down for a game of soloqueue, I start the matchmaker and glance at my profile. Silver III, 76 LP. Two wins would take me to promos. A little over a minute later, I enter champion select and spot a troll. I dodge. I now have 73 LP. I still need two wins, so the dodge was free. In fact, after waiting 5 minutes and re-queuing, I spot another troll and dodge again. I now have 63 LP, but because a win grants about 20 LP, I still need only two to reach 100. So, both dodges were free.
Since a win grants one block of 20 LP, every 20 LP from 0 to 100 is effectively a hidden breakpoint in each division. Whenever dodging would not cost so many LP as to put you below a breakpoint, you are free to dodge without increasing the number of wins you need to reach promos.