Unless your lid is especially tight-fitting, you’d do well to completely ignore pressure effects on the boiling point. This site gives the data on the relationship between boiling point and pressure for water.
To raise the boiling point of water one single degree Fahrenheit, to 213 °F at sea level, you need to raise the pressure in your vessel by 0.3 psi. This may not sound like much, but on a 12" diameter lid, that means a force of 34 lbs pushing it up. And that’s for just one degree! If you wanted to raise the boiling point to something you might consider noticeably different, say 230 °F, you’d need a lid that could hold the inside more than 6 psi higher than the outside. That’s over 700 lbs of force on the 12" lid.
Suffice it to say that a normal lid can’t seal well enough to make any noticeable difference in boiling point by raising the pressure.
What the lid does well, however, is contain the hot gas above the liquid, reducing heat loss to convection. A shiny lid may also help by reflecting infrared radiation back into the container, instead of letting it radiate away into the kitchen.
So a lid helps reduce heat loss and lets the water boil faster. But it doesn’t delay boiling by increasing the pressure, because pot lids are horrible pressure containment devices.