ETRTO size tolerance - can I mount a 62-203 tire instead of 54-203?
The first number refers to the tire width: 62mm versus 54mm for the tires you're looking at.

Will this tire fit? Probably but...

The tire will fit on the rim but the question is whether the larger tire will fit in the bicycle safely.

Manufacturers are infamous in misstating tire widths so your current tires may be less than 54mm (2") and the 62mm tires may be larger.

Because you're looking at going larger you need to check if there is sufficient clearance for the new tire which should be about 4mm wider on each side and about 4mm taller. 

So my recommendation is to check the amount of space you have in all of the places the tire passes the frame/fork. For example with the fork I will check clearance to the side AND between the tire and the fork crown.  For the rear wheel I will check at the seat stays and chain stays. Again checking both vertical and horizontal clearance.

To check clearance I use the two flat sides of an allen wrench as a feeler gauge. For a bike which will be running a 54mm tire you'll probably want a minimum of 10 to 12 mm of clearance for mud so I'd be using a 5/8" (15.9 mm) allen wrench to check clearance with the current tire.  If the bike won't be used in muddy conditions then you can certainly go with less clearance to the frame.

If OTOH you opt for a slightly narrower tire then it'll fit fine.