I like to run a lethal campaign, so I allow for higher stats to help the PCs survive.
Which is it? Those are directly conflicting statements.
What you are describing is not a campaign that is more lethal, but one that might appear more lethal on its surface because the numbers in use are larger: +7 to a d20 roll or an average 10 damage look larger than +5 to a d20 roll or an average 8 damage, but that is only actually true if the other side of the equation is unchanged - d20+7 vs. DC 15 is
the same as d20+5 vs. DC 13, not higher, and 10 damage from 40 hit points is
the same as 8 damage from 32 hit points.
If your goal is to actually make the game more lethal, leaving the players as-standard and then scaling up the threats they face is all that is needed. Scaling both equally just inflates the visible numbers without actually altering anything meaningful, and scaling both but doing it unequally is wasted effort over just scaling one side by a lesser degree.
Sorry if I come of as harsh about this, I've got a thing about DMs that do what you have described, developed from seeing so many of them in my own gaming life that would invent all this extra work for themselves of trying to add stuff to the PCs like bigger stats, better gear, and higher hit points just to entirely invalidate the purpose of those alterations by ramping up the challenges faced... and then the campaign falls apart because the difficulty of properly compensating for changes to one side by changing the other distracts the DM from other parts of running a game, or the players manage to not have fun in the campaign whether it is because they have these "uber characters" on paper that are being made to look like incompetent newbs and resulting in a feeling that no character could possibly actually succeed and do well in the DM's campaign, or because the DM has provided not the more lethal game desired, but a game where it seems the characters might as well officially be unbeatable immortals without a care in the world because the DM can't actually find a way to challenge them and then gets tired of trying.