I don't think so. The United Kingdom is one of the donor nations within the EU, and they help to subsidize the poorer nations such as Poland and Lithuania. If the Brexit occurs for real, then the pressure on the other donor nations (such as Germany, Netherlands, and France) will increase significantly. They are already under a lot of strain as a result of the Greek bailout.
Not sure why you mentioned Lithuania as "poorer". At 2016 index of economic freedom Lithuania ranks 13th in the world and 6th in Europe
http://www.heritage.org/index/rankingThis country has received from the EU 10765 million over what it has contributed(small amount comparing to many other EU countries), for example:
Poland - got 74296 million over what it has contributed
Portugal - got 63579 million over what it has contributed
Spain - got 91463 million over what it has contributed
Greece - got 109258 million over what it has contributed
More stats can be found:
http://www.money-go-round.eu/