Any person that brings up Dick Butkus in a discussion of NFL football in 2015 is the one who is dumb. For those old enough to have seen, Butkus was a shadow of his former self at the end of his career (and that was at the ages of 30-31). Regardless, that was 45 years ago and it's not relevant now.
Besides, Lance Briggs is not Dick Butkus.
I'll grant you Justin Smith, but he is the exception to the rule. Successful NFL teams simply do not field 35 year old players and win. Also, Smith plays DT and is on the field for a much smaller percentage of the snaps. It's a position that is predicated on strength, leverage, situational football and gap assignments. That's much different that playing ILB which is much more reliant on speed and the ability to cover much younger, faster tight ends and are required to be on the field for a considerably higher percentage of snaps Last time I checked, 35 year old Justin Smith isn't responsible for covering Gronk or Jimmy Graham or spying Russell Wilson.
There are very few positions in the NFL where a player can be effective after say 34. Manning and Brady are defying Father Time (although Manning not so much) at the QB position. Kickers are kickers. DT is the one position where aging guys who can play limited snaps and don't rely on speed (Smith, Wilfork) can play later into their 30s.
Lance Briggs is not a DT.