I would go for FILTER and VLOOKUP combined together.
First you need to filter the range to remove all the values older than 2 months and then do the vlookup.
=vlookup(F3,filter(C2:D,B2:B>edate(today(),-G1)),2,false)
edate(today(),-g1) gives you the date 2 months before today
filter(C2:D,B2:B>edate(today(),-G1)) makes a range without entries older than 2 months.
Vlookup looks for entries "billy" in temporary filtered range and returns it's 2nd column.
Remember: If there are more entries within 2 months period, vlookup will show only first one from the list. If you want all entries you should use filter function with 2 conditions.
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