▁of ▁the ▁ 2 0 1 0 ▁United ▁States ▁Census , ▁the ▁population ▁was ▁ 1 9 , 6 8 7 . ▁Its ▁county ▁seat ▁is ▁Lib by . ▁The ▁county ▁was ▁founded ▁in ▁ 1 9 0 9 ▁and ▁named ▁for ▁President ▁Abraham ▁Lincoln . ▁The ▁county ▁lies ▁on ▁Mont ana ' s ▁north ▁border ▁and ▁thus ▁shares ▁the ▁US - Can ad ian ▁border ▁with ▁the ▁Canadian ▁province ▁of ▁British ▁Columbia . ▁ ▁This ▁heavily ▁wood ed ▁and ▁mountain ous ▁county ▁once ▁was ▁part ▁of ▁Fl at head ▁County ▁until ▁residents ▁of ▁Lib by ▁and ▁E ure ka ▁pet ition ed ▁the ▁state ▁legisl ature ▁for ▁separation . ▁Lib by ▁won ▁an ▁election ▁over ▁E ure ka ▁to ▁host ▁the ▁county ▁seat . ▁ ▁Geography ▁According ▁to ▁the ▁US ▁Census ▁Bureau , ▁the ▁county ▁has ▁a ▁total ▁area ▁of ▁, ▁of ▁which ▁ ▁is ▁land ▁and ▁ ▁( 1 . 7 %) ▁is ▁water . ▁The ▁county ▁borders ▁the ▁Canadian ▁province ▁of ▁British ▁Columbia ▁to ▁the ▁north . ▁The ▁lowest ▁point ▁in ▁the ▁state ▁of ▁Mont ana ▁is ▁located ▁on ▁the ▁K oot en ai ▁River ▁in ▁Lincoln ▁County , ▁where ▁it ▁flows ▁out ▁of ▁Mont ana ▁and ▁into ▁Id aho . ▁Up stream , ▁Lib by ▁Dam ▁back s ▁up ▁huge ▁Lake ▁Ko oc an usa ▁( com bin ation ▁name ▁of ▁K oot en ai , ▁Canada , ▁USA ) ▁into ▁Canada ' s ▁British ▁Columbia . ▁ ▁Ad j acent ▁count ies ▁and ▁county - equ ival ents