Lan has been trained by the best in the Borderlands since his cradle. Twenty years ago he took on six at once and lived, even Rand can't do that with the Power to sharpen him. Twenty years ago he beat the best. Sure he's older now but he's got twenty years more experience. Add in the benefits of being a Warder and I say he could take Birgitte. Mat might beat him, but only through his luck.