Originally Posted by
BFisher
Also, typically the chain and freewheel should be changed together, as they both wear and a new chain on a worn freewheel can produce problems.
This is not entirely true. A "stretched" chain will destroy a freewheel but as long as you change the chain before it gets beyond wear limits, your freewheel will live through many, many chains.
Before buying a new chain, you should measure your existing chain using a steel rule or a tape measure to determine if it is actually worn out. Sheldon explains how here:
https://www.sheldonbrown.com/chain-wear.html
If the chain is not worn out, then just clean it thoroughly and lube it.
Now, back to the original issue...
It's unlikely that a sudden problem getting into lower gears will have anything to do with having a worn chain. I'm wondering if you have another mechanical problem such as a bent part or a broken spring in the derailleur.