The difference between 3.5e and 5e mechanically - are pretty great. Particularly as 5e introduces the "advantage / disadvantage" mechanic, which doesn't really have a close equivalent in 3.5e (yes, the Luck domain power can let you reroll a d20, and there's some other d20 trickery around as well, but it isn't really the advantage / disadvantage mechanic).
On page 3, LMoP says that DC10 is Easy, DC15 is Moderate, and DC20 is Hard. That's fair, and should work fine in both 5e and 3.5e. However, as you're going towards 5th level with the player characters (LMoP is meant to go from 1st to 5th, roughly), you may see that 3.5e increases in a different way as compared to 5th edition.
A 5th level 3.5e character can be expected to hit a bonus of about 10 - 15 pretty easily in a class skill, (+2/+3 from attribute, 8 ranks, perhaps a Synergy +2 and a Misc +2) and will therefore start hitting higher DCs consistently as compared to a 5th level 5e character. At 1st - 3rd level, I'd say the difference between 3.5e and 5e when it comes to DCs, is largely something you can ignore.
Goblins are goblins. Replacing them should be fine. Treasure is treasure - but I should also caution that I find 3.5e is more item-driven than 5e, so you should take a stock of things when LMoP is done, and perhaps up the treasure slightly at 4th and 5th level (slightly more potions, perhaps a scroll or two more, maybe slightly more powerful arms and armor).
Not that monsters - in particular undead and plant-based monsters - have different immunities in 5e as compared to 3.5e. The humans and orcs can be used much as they're written up in the module; you don't really need to do much there at all. Same goes for the ogre, and most other humanoids in the list.
I suspect the immunities and resistances of the dragon are quite different as well - but it's not an immediate issue, and you can look at it when you get there.
Attack bonuses start diverging once you level up a couple of times as well, but for NPCs it doesn't really matter much between 1st and 5th level. For NPCs of higher HD, you might want to recalculate attack bonuses though, based on their BAB and so on, in order to keep things challenging.
XP is a bit of a sore point. If the party starts lagging behind the suggested power curve, make sure that you're giving out enough XP. Also, consider giving out bonus XP (a hundred here, a couple hundred there) for particularly good and/or entertaining roleplaying. An RPG session shouldn't be death by spreadsheet - it should be fun, whichever system you're using.
So in short - yes, you can keep the DCs as suggested, you can keep the monsters pretty much as suggested, but you need to look at resistances and immunities, and towards the higher bracket you need to look at attack bonuses. You should also keep an eye on the treasure given (and possibly increase it), and if the party starts lagging behind you should consider upping the XP given.
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