The short answer is “no;” the products of a Eucharistic miracle such as the one in Lanciano, no longer have the substantial and sacramental presence of Christ.
A little background on how the Eucharist “works” in the Catholic and Orthodox churches
For the benefit of readers, here is a very short primer on the belief shared by Catholics and the Orthodox (and the Oriental Orthodox, Assyrian, Polish National Catholic Church, etc.) on the Eucharist.
These churches all believe that when a priest or bishop consecrates the bread and wine, these species are converted into Jesus Christ. In Western terminology (not commonly used in the East), we say that the very substance of the bread and wine is converted into the substance of Jesus. In other words, after the consecration (or epiclesis, in the Eastern rites), the sacred species cease to be bread and wine, and from that moment on are Jesus Christ. In Western terminology, this conversion is called transubstantiation. (See Catechism of the Catholic Church [CCC] 1376.)
The Eucharistic species, however, retain all of the properties and appearances (or “accidents”) of the bread and wine; hence, they are indistinguishable from bread or wine chemically and physically. (See Council of Trent, Session XIII, Decree on the Eucharist, Can. 2; see also Summa theologiae [S.Th.], III, q. 75, a.5.)
It is important to note that the substantial presence of Christ ceases as soon as they cease to have the appearance of bread or wine. For example, once the bread is dissolved into a paste, or the wine is diluted, the Real Presence ceases. (See CCC 1377, as well as S.Th. III Pars, q. 77, a. 4, responsum, and my answer to the question During communion, when does the wafer stop being Jesus' body?)
Regarding the Eucharistic miracles
In the case of miracles such as those at Lanciano (i.e., in which either the bread becomes actual human flesh or the wine becomes human blood), it is clear that the appearance of bread or wine has ceased, albeit in an extraordinary way. The object in question now has the properties of human flesh or human blood, not bread or wine.
It follows that these objects no longer have the sacramental presence of Christ—however extraordinary they are.