Often. LMT just says, this price or better. What you see in a retail broker and a consumer internet connection is delayed. Timeline example in ms:
T-0: A trade at Price X occurs at exchange.
T+250: The broker process it.
T+400: It gets to your machine
T+800: You react and put in your order MKT
T+1200: your order is accepted at broker
T+1450: order is live at exchange. (IB claims 250ms transmit time)
T+1700: Order executes after all the other MKT order before you execute.
These are just examples times, but you get the idea. For a LMT order, the MKT orders go first, then all the other LMT orders before you.
That is why RobinH is a thing, they sell your order flow and all sorts of stuff can happen in 250 ms. Meanwhile people think it is like retail purchasing at an Apple store and watch animated graphics for entertainment. But in the background....
Your trading plan has to take this into account.