recently和lately“最近，近来”，常与完成时搭配。这两个词均不表示具体的或特定的时间节点，所以不与since搭配。如果是具体的时间节点则可以用since,如：

I have not seen him since then.从那以后我再也没见过他。

I haven't seen my own daughter since last January.自去年1月起我就没见过女儿了。

要表示“自从最近以来”，英语可以说 since recently, since lately 吗？

recently, lately 都是表示抽象时间的副词,以上都是表示最近,进来,因此不能再在加since,  recently, lately 一般与现在完成时连用，since+表示具体时间点时间名词和具体时间副词

(1)lately adv.  近来，最近; 不久以前

Dad's health hasn't been too good lately. 

爸爸的健康状况近来不太好。

Lord Tomas had lately been appointed Chairman of the Centre for Policy Studies. 

托马斯勋爵最近被任命为政策研究中心主席。

(2)recently  adv.  最近，近来; 不久以前; 近日; 新近

The bank recently opened a branch inGermany. 这家银行最近在德国开设了分行。

It is only fairly recently that historians have begun to investigate the question. 

只是到最近历史学家才开始探究这个问题。

汉语中不存在“自从最近以来”这种表达。

在英语中不可以说 since recently, since lately 。